For each of the following equations, solve for the variable. If there are multiple solutions, separate them by a comma.
Answers should be integers, fractions, radicals, or in exponential form. No decimals!
1/7㏒ (x-1) + 3㏒ (2)
x=______
3㏑(ω+6) = 5㏑ (6)
ω=____

Answer:

Step-by-step explanation:

Answer:

11.6 years

Step-by-step explanation:

Given

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

we can solve for [tex]t[/tex]

[tex]t=\frac{ln(\frac{A}{P} )}{n*ln(1+\frac{r}{n}) }[/tex]

We are given

[tex]A=1800\\P=900\\r=0.06\\n=12[/tex]

We can evaluate [tex]t[/tex].

[tex]t=\frac{ln(\frac{1800}{2} )}{12*ln(1+\frac{0.06}{12}) }[/tex]

[tex]t=11.6[/tex]

Answer:its 30 ft

Step-by-step explanation:

easyyy

In 2000, the population of the state was 23.1 million and the population of the state reach 28.3 million in 2013

From the question, we have the following parameters that can be used in our computation:

A=23.1 е⁰⁰¹⁵²⁺

Also from the question, we have

The variable t represents the number of years after 2000.

This means that

t = Current year - 2000

Substitute the known values in the above equation, so, we have the following representation

t = 2000 - 2000

Evaluate

t = 0

So, we have

A=23.1 е⁰⁰¹⁵² ˣ ⁰

Evaluate the above equation

A = 23.1

Here, we have

A = 28.3

Substitute the known values in the above equation, so, we have the following representation

23.1 е⁰⁰¹⁵²⁺ = 28.3

Divide both sides by 23.1

е⁰⁰¹⁵²⁺ = 1.22510822511

Take the natural logarithm of both sides

0.0152t = 0.203

So, we have

t = 0.203/0.0152

Evaluate

t = 13

So, the year is

Year = 2000 + 13

Year = 2013

This means that the population of the state reach 28.3 million in 2013

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If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Conversion means converting the same thing into different units.

Home Depot sells boards in 3-meter lengths. If you only need 1 meter and 45 cm. Then the length that you need is calculated as,

⇒ 1 meter and 45 centimeters

Convert the centimeters into a meter. Then we have

⇒ 1 + 45 / 100

⇒ 1 + 0.45

⇒ 1.45

Then the length of the board left will be calculated as,

⇒ 3 - 1.45

⇒ 1.55 meters

If you only need 1 meter and 45 cm. Then the length of the board left will be 1.55 meters.

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True. An ordinary regression (or ANOVA) model that treats the response Y as normally distributed is a special case of a GLM, with a normal random component and identity link function.

A flexible framework for modeling the relationship between a response variable Y and one or more predictor variables X is called a generalized linear model (GLM).

A GLM model allows for the use of non-identity link functions as well as for the response variable to have a distribution other than the normal distribution.

If we consider an ordinary regression model or an analysis of variance (ANOVA) model that assumes a normal distribution of response variable Y, this can be considered a special case of a GLM, with the normal distribution as the random component and the identity link function.

Here,  the variance of the response is assumed to be constant, and the mean of the response variable is assumed to be a linear function of the predictor variables.

Let

Y ~ N(μ,σ²)

μ = β₀ +β₁X₁ + β₂X₂ + ... + βₙXₙ

In this case, a normal distribution, with mean μ and variance σ² id followed by response variable Y.

here we can see that the mean μ is a linear function of the predictor variables X₁, X₂, ..., Xₙ, with coefficients β₀, β₁, β₂, ...,βₙ.

The identity link function, that is, that μ is equal to the predicted value of Y is used.

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The number of races that were 10-kilometer long is 102.

An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.

Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.

32×15 + 10x = 1,500

480 + 10x = 1,500

10x = 1,500 - 480

10x = 1,020

x = 1,020/10

x = 102

Hence, the number of races that were 10-kilometer long is 102.

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Answer:

x=6

Step-by-step explanation:

6x-16=20

Add 16 to both sides

6x-16=20

    +16. +16

6x=36

Divide 6 to both sides

6x=36

/6. /6

x=6

Hopes this helps please mark brainliest

Answer:

x = 6

Step-by-step explanation:

Given equation,

→ 6x - 16 = 20

Now the value of x will be,

→ 6x - 16 = 20

→ 6x = 20 + 16

→ 6x = 36

→ x = 36/6

→ [ x = 6 ]

Hence, the value of x is 6.

Answer: 6

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.  

Input the numbers that you are given.

|(2)(7)|−(−4) / 3    (Input the numbers)

=|14|−(−4) / 3       (Multiply your numbers, then you get 14.

=14−(−4) / 3     (find the absolute value (always will be positive) )

=18/3           (Change the fraction into a whole number)

=6

The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."

Given : 40 - 4x > 10 which is an inequality

To find : The value of x

Procedure:

Step 1:  Collect all the terms with x on right side and the constant terms  on the left side of the greater sign.

40 - 4x > 10

When 10 is brought to the left, there will be change in sign for the number 10 and similarly, when -4x is taken to the right, it becomes +4x or simply 4x. So inequality becomes

40 - 10 > 4x

Step 2: On solving the resulting inequality, we get

30 > 4x

Divide both sides by 4. So inequality becomes

[tex]\frac{30}{4} > \frac{4x}{4}[/tex]

7.5 > x

This means, x < 7.5

The choice that best describes the number of smoothies that Savannah could buy between now and the end of this month with her gift card balance is "She can buy from 0 to 7 smoothies, but no more."

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Answer:She can buy from 0 to 7 smoothies, but no more."

Step-by-step explanation:She can buy from 0 to 7 smoothies, but no more." Which is option B

A rectangle is one of the types of four sided figures generally refers to as quadrilaterals. The required proof is as stated below:

Rectangles, Parallelograms, square, trapezium, kite and rhombus are a family of quadrilaterals, since they all have four straight sides. Each of these figures have individual properties that can be used to differentiate one from the other.

Some peculiar properties that can be used to identify a rectangle are:

Therefore to prove that IJKL is a rectangle;

<1  ≅  <2 (Given)

IL ≅ JK (opposite sides are equal)

IJ  ≅  LK (opposite sides are equal)

IK  ≅ JL (diagonals have equal length)

M is the midpoint of IK and JL respectively.

<JIK  ≅ <IKL (alternate angles property)

<IJL  ≅  <KLJ (alternate angles property)

IL ⊥ IJ

IJ ⊥ JK

JK ⊥ LK

LK ⊥ LI

Therefore, the given figure is a rectangle.

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Answer:

x = 64

Step-by-step explanation:

63.         28

----    =    ----

144.         x

Now cross multiply:

144(28) = 63(x)

4,032 = 63x

x = 64

May I have a brainliest? Thank you!

Answer:

C

Step-by-step explanation:

Linear Function- points on a graph that make up a straight line negative or positive.

Only Values of (C) makes a perfect line.

a) The best estimate of the probability of rolling a "6" with this die is

0.2 (100/500).

My best estimate of the probability of rolling a “6” is 20%. This is calculated by taking the number of “6”s rolled in the 500 trials (100) and dividing it by the total number of trials (500).

b) If you roll this die 30 times, you can expect to get 6 "6"s (0.2 x 30).

If I roll this die 30 times, I expect to get 6 “6”s. This is calculated by taking the probability of rolling a “6” (20%) and multiplying it by the number of trials (30).

c) If you roll a fair die 30 times, you can expect to get 5 "6"s (1/6 x 30).

If I roll a fair die 30 times instead of the “unfair” die, I expect to get 5 “6”s. This is calculated by taking the probability of rolling a “6” on a fair die (16.7%) and multiplying it by the number of trials (30).

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0.0395 m, -0.486 ms⁻¹ and -4725.791 ms⁻² are the position, velocity and acceleration of the particle are  respectively

Given that:

A particle moves so that position in meters is given as a function of time in seconds by the equation x(t)=Acos(wt+l), where A=0.0395 m, w=346 s⁻¹, and l=1.00

The position of the particle at 3.00 ms

Substitute t = 3.00 ms = 0.003 s into the function:

x(t) = Acos(wt+l)

x(0.003) = 0.0395cos(346×0.003 + 1.00)

x(0.003) = 0.0395cos(2.039)

x(0.003) = 0.0395 m

The velocity of the particle at 3.00 ms

To get the velocity function, take the derivative of x(t) = Acos(wt+l):

x'(t) = -Awsin(wt+l)

Then substitute t = 3.00 ms = 0.003 s into the velocity function:

x'(t) = -Awsin(wt+l)

x'(0.003) = -0.0395 ×346sin(346×0.003 + 1.00)

x'(0.003) = -13.667sin(2.038)

x'(0.003) = -0.486 ms⁻¹

The acceleration of the particle at 3.00 ms

To get the acceleration function, take the derivative of x'(t) = -Awsin(wt+l):

x''(t) = -Aw²cos(wt+l)

Then substitute t = 3.00 ms = 0.003 s into the  function:

x''(t) = -Aw²cos(wt+l)

x''(0.003) = -0.0395 ×346² cos(346×0.003 + 1.00)

x''(0.003) = -4728.782 cos(2.038)

x''(0.003) = -4725.791 ms⁻²

Therefore, the position, velocity and acceleration of the particle are 0.0395 m, -0.486 ms⁻¹ and -4725.791 ms⁻² respectively

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a) Corresponding angles are congruent, m<a=139

b) Alternate Interior Angles are congruent, m<b =139

x = 12, using the concept of absolute value equation.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.

To answer an absolute value problem, isolate the absolute value on one side of the equation. Then, resolve both equations by setting their respective contents to the positive and negative values of the integer on the other side of the equation. 

Given that,

4|x+6| = 24

either |x+6| = 6 or,  |x+6| = -6

x = 0. -12

So, x = 12                           [here as negative sign is already present]

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Answer:

Step-by-step explanation:

23-15=8 (pour savoir combien elle a dépenser en tout)

8 diviser par 2= 4 (pour savoir le prix d'un stylo)

chaque stylo vaut 4 $

The estimate of the average height of all the trees having a trunk diameter of 7 inches is y = 18.1 feet. This is obtained by using the LSRL equation. Option A is the correct value.

The LSRL equation is defined as the Least squares regression line. This is the line that minimizes the variance. So, it is the best line of fit for a set of data points.

The equation is in the form of Y = a + bX

Here a is the intercept and b is the slope.

It is given that,

X is given as the diameter of a tree trunk in inches

Y is given as the tree height in feet

The given data points are:

X: 4, 2, 8, 6, 10, 6

Y: 8, 4, 18, 22, 30, 8

For these data points, the least squares regression line is given by the equation Y = - 3.6 + 3.1X

So, the estimate of the average height of all trees having a trunk diameter of 7 inches is

Y = - 3.6 + 3.1X ⇒ Y = -3.6 + 3.1 × 7

⇒ Y = -3.6 + 21.7

∴ Y = 18.1 feet

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The  average rate of change of the function from x = 1 to x = 4 is 14.90

A function can be defined as an expression, law or rule that shows the relationship between two variables.

The variables are;

Given the function;

f(x) = 10x^2 + x

For x = 1, let's substitute the value of x as 1

f(1) = 10(1)^2 + 1

f(1) = 10 + 1

f(1) = 11

For  x = 4, let's substitute the value of x as 4

f(4) = 10(4)^2 + 4

f(4) = 10(16) + 4

f(4) = 160 + 4

f(4) = 164

The rate of change = 164/11 = 14. 90

Hence, the value is 14. 90

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The answer to this Question based on pH is 8.12

What is pH?

pH is a measure of acidity or basicity in a solution. It is measured on a scale ranging from 0 to 14, with 7 being neutral. A pH below 7 is acidic and a pH above 7 is basic. A solution with a pH of 0 is the most acidic, while a solution with a pH of 14 is the most basic. The pH of a solution is an important factor in many chemical and biological processes, as it affects the activity of molecules. For example, enzymes typically only function within a certain pH range, and most biological cells have a preference for a specific pH. pH is also important in determining the solubility of certain substances, and can affect the taste of food.

Here [H] = 7.7 * 10^-9

pH = -log[7.7 * 10^-9]

using some log properties this value comes out to be

pH = 9 - 0.88

pH = 8.12 and pH greater than 7 means solution is Basic

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a. The population of the state in 2000 is 18.5 million

b. The population will reach 26.6 million in about 2 years

From the question, we are to determine the population of the state in 2000.

From the given information,

The formula that models the population of the US state after 2000 is

A = 18.5e^(0.1708t)

To determine the population of the state in 2000, we will substitute t = 0

That is,

A = 18.5e^(0.1708(0))

A = 18.5e^(0)

A = 18.5(1)

A = 18.5

Thus, the population of the state in 2000 is 18.5 million

b. To determine when the population will reach 26.6 million

Substitute A = 26.6 in the equation

A = 18.5e^(0.1708t)

26.6 = 18.5e^(0.1708t)

Solve for t

26.6/18.5 = e^(0.1708t)

ln(26.6/18.5) = 0.1708t

0.36314048 = 0.1708t

t = 0.36314048/0.1708

t = 2.126

t ≈ 2

Hence, the population will reach 26.6 million in about 2 years

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Answer:

y = 14

Step-by-step explanation:

y = k[tex]\sqrt{x}[/tex]  Solve for k

7 = k[tex]\sqrt{9}[/tex]

7 = k3  Divide both sides by 3 to solve for k

[tex]\frac{7}{3}[/tex] = k  

y = kx

y  = [tex]\sqr\frac{7}{3} }[/tex][tex]\sqrt{36}[/tex]

y = [tex]\frac{7}{3}[/tex](6)

y = 14

[tex]\frac{7}{3}[/tex][tex](\frac{6}{1})[/tex] is the same thing as [tex]\frac{7}{1}[/tex][tex](\frac{2}{1})[/tex]  I cross canceled the 3 and the 6

[tex]\frac{14}{1}[/tex] = 14

Answer:

Step-by-step explanation:

Find the equation of lines m, n and p

                    The equation of line:      

                       [tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

Line m: (-3,2)  (3,6)

x₁=-3   x₂=3   y₁=2   y₂=6

[tex]\displaystyle\\\frac{x-(-3)}{3-(-3)} =\frac{y-2}{6-2} \\\\\frac{x+3}{3+3} =\frac{y-2}{4} \\\\\frac{x+3}{6}=\frac{y-2}{4}[/tex]

Multiply both parts of the equation by 4:

[tex]\displaystyle\\\frac{x+3}{6}(4)=y-2\\\\\frac{2}{3} (x+3)=y-2\\\\\frac{2}{3}x+2=y-2\\\\\frac{2}{3}x+2+2=y-2+2\\\\\frac{2}{3}x+4=y\\\\Thus,\ y=\frac{2}{3} x+4\\\\Hence,\ m_m=\frac{2}{3}[/tex]

Line n: (-5,-5)  (5,1)

x₁=-5   x₂=5   y₁=-5   y₂=1

[tex]\displaystyle\\\frac{x-(-5)}{5-(-5)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+5}{5+5}=\frac{y+5}{1+5} \\\\\frac{x+6}{10}=\frac{y+5}{6}[/tex]

Multiply both parts of the equation by 6:

[tex]\displaystyle\\\frac{3}{5}( x+5)=y+5\\\\\frac{3}{5} x+3 =y+5\\\\\frac{3}{5} x+3-5=y+5-5\\\\\frac{3}{5} x-2=y\\\\Thus,\ y=\frac{3}{5}x-2\\\\Hence,\ m_n=\frac{3}{5}[/tex]

Line p: (3,-4)  (-3,6)

x₁=3   x₂=-3   y₁=-4   y₂=6

[tex]\displaystyle\\\frac{x-3}{-3-3} =\frac{y-6}{6-(-4)} \\\\\frac{x-3}{-6} =\frac{y-6}{6+4} \\\\\frac{x-3}{-6}=\frac{y-6}{10} \\[/tex]

Multiply both parts of the equation by 10:

[tex]\displaystyle\\-\frac{5}{3} x+5=y-6\\\\-\frac{5}{3} x+5+6=y-6+6\\\\-\frac{5}{3} x+11=y\\Thus,\ y=-\frac{5}{3}x+11 \\\\Hence,\ m_p=-\frac{5}{3}[/tex]

[tex]Question# 5: \ m_m\neq m_n\ \ \ \ m\ isn't\ parallel \ to\ n\\\\Question# 6:\ m\ isn't \ congruent \ to\ p\\\\Question#7 :\ n\ isn't \ congruent \ to\ p[/tex]

[tex]n \bot p[/tex]

Answer:

5) No the lines are not parallel because in order for this to be true, the slopes have to be equal. Line m has a slope of 2/3 and line n has a slope of 3/5. Both slopes are not equal so it is not parallel

6) No, m is not congruent to p

7) No, n is not congruent to p

(Is there any chance that you meant to say perpendicular instead of "congruent"?)

Step-by-step explanation:

For two lines to be parallel the slopes have to be equal

See attached to see the rise over run

line m: 2/3

line n: 3/5

The slopes are not equal so the lines are not parallel.

18.5 is correct for part (a) since t = 0 leads to A = 18.5

=====================================================

Part (b)

Your teacher is asking for the value of t when A = 26.6

A = 18.5*e^(0.1708t)

26.6 = 18.5*e^(0.1708t)

26.6/18.5 = e^(0.1708t)

1.437838 = e^(0.1708t)

Ln(1.437838) = 0.1708t

t = Ln(1.437838)/0.1708

t = 2.126116 approximately

t = 2 when rounding down to the nearest integer

Therefore, 2 years after the year 2000, the year 2002, is when the population reaches roughly 26.6 million. The actual population will be slightly less than 26.6 million, but it's close enough.

Note that:

which helps confirm the correct value of t is between t = 2 and t = 3.

The values to make up the solution set of inequality are {8,9,10}.

In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality.

A less than symbol (a, b) denotes that one thing is less than the other.

The notation a > b indicates that an is greater than b.

A and b are not equal in either situation. A strict inequality is one in which an is strictly less than or strictly bigger than b in certain connections. Comparability is left out.

First we have to replace m with 8, it becomes:

8+7 =15<18

For 9,  

9+7 =16<18

For 10,

10+7 =17<18

And for 11,

11+7 =18=18

So, The values to make up the solution set of inequality are {8,9,10}.

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The points on the coordinate grid are been labelled in the image attached with solution.

A pair of integers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. The terms abscissa and ordinate are used to describe the x- and y-coordinates, respectively. A point in a plane is represented by both coordinates (x, y).

Here,

The picture showing the answer is labeled with the coordinate grid's points.

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The value of variable x is 19.20.

Let's find the value of variable x in the equation.

A variable is a number represented with letters in an equation.

Therefore,

x / 6 + 4 / 10 = 3 + 6 / 10

Therefore, let's find the variable x.

10x + 24 / 60 =  30 + 6 / 10

10x + 24 / 60 = 36 / 10

60 × 36 = 10(10x + 24)

2160 = 100x + 240

2160 - 240 = 100x

1920 = 100x

divide both sides by 100

x = 1920 / 100

x = 19.20

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Answer: its A 23.04

Step-by-step explanation:

The value of expression  13 1/3 divided by 2/3 would be; 20

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the expression of 13 1/3 divided by 2/3

Therefore,

40/3 divided by 2/3

40/3 x 3/2

20

Therefore, The value of expression  13 1/3 divided by 2/3 would be; 20

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The solution set for absolute value inequalities are presented as follows;

(b) (i) -∞ < x ≤ 2

(ii) 1.25 ≤ x < 3, or x > 3

An absolute value inequality is an inequality with an absolute value expression containing a variable.

(i) |2·x + 7| + 1 ≥ 6·x

Solving for when |2·x + 7| is positive, we get;

2·x + 7 + 1 ≥ 6·x

7 + 1 ≥ 6·x - 2·x = 4·x

8 ≥ 4·x

Dividing both sides by 4, we get;

8 ÷ 4 ≥ 4·x ÷ 4 = x

2 ≥ x

Therefore; x ≤ 2

The solution of the absolute value inequality can be found as follows;

|2·x + 7| + 1 ≥ 6·x

|2·x + 7| ≥ 6·x - 1

Therefore, we have the following compound inequality;

2·x + 7 ≤ -(6·x - 1), 2·x + 7 ≥ (6·x - 1)

The solution for the inequality, 2·x + 7 ≤ -(6·x - 1) is found as follows;

2·x + 7 ≤ -(6·x - 1) = 1 - 6·x

2·x + 6·x ≤ 1 - 7 = 6

8·x ≤ 6

x ≤ 6/8 = 3/4

x ≤ 3/4

The solution for the inequality, 2·x + 7 ≥ (6·x - 1) is found as follows;

2·x + 7 ≥ (6·x - 1)

7 + 1 ≥ 6·x - 2·x = 4·x

8 ≥ 4·x

x ≤ 2

Combining the solution, we get;

-∞ < x ≤ 2

(ii) [tex]\left|\dfrac{2\cdot x+ 1}{x - 3} \right| \geq 2[/tex]

Therefore, we get;

[tex]\dfrac{2\cdot x+ 1}{x - 3} \leq -2[/tex]

[tex]\dfrac{2\cdot x+ 1}{x - 3} + 2 \leq 0[/tex]

[tex]\dfrac{4\cdot x - 5}{x - 3} \leq 0[/tex]

x < 3, or x ≥ 1.25

1.25 ≤ x < 3

[tex]\dfrac{2\cdot x+ 1}{x - 3} \geq 2[/tex]

[tex]\dfrac{2\cdot x+ 1}{x - 3} -2 \geq 0[/tex]

[tex]\dfrac{7}{x - 3} \geq 0[/tex]

Therefore, x > 3,

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