Solve the |4X -5|= |-X +5|

Answers

Answer 1

Recall the definition of absolute value:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Then we have a few cases to consider:

• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to

[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]

• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get

[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]

• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then

[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]

but we already have this solution.

• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then

[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]

which we also already found.


Related Questions

A raised flower bed is 40 feet​ long, 7 feet​ wide, and 1.2 feet deep. Find the area of the bed and the volume of soil it holds.

Answers

Area = length x width

Area = 40 x 7 = 280 square feet

Volume = length x width x depth

Volume = 40 x 7 x 1.2 = 336 cubic feet

how about these are they correct?​

Answers

Yes, all three are correct

-355 - 165 = - (355+165) = -520

-150 - 126 = - (150+126) = -276

-201 - 124 = - (201+124) = -325

P/s: they are wrong. you need this " () "

ok done. Thank to me :>

matthew drove 252 miles to his familys vacation spot his father drove twice as many miles and then thy arrived at their hotel how far did the family travel to get to their destination

Answers

i’m not sure if it’s right but this is what i got

252
252x2 =504
504+252
756 miles?

From a hot-air balloon, Grayson measures a 29^{\circ} ∘ angle of depression to a landmark that’s 1004 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Answers

The balloon’s vertical distance above the ground is 556 feet

The set up will form a right triangle.

Given the following parameters

Angle of depression = 29 degreesHorizontal distance = 1004 feet

To get the height above the ground, we will use the SOH CAH TOA identity as shown;

Opposite = h

Adjacent = 1004 feet

Tan theta = h/1004

Tan 29 = h/1004

h = 1004 tan 29

h = 1004(0.5543)

h = 556.52 feet

Hence the balloon’s vertical distance above the ground is 556 feet

Learn more on angle of depression here: https://brainly.com/question/23497407

2. Kiant is having a sale on ketchup. All
ketchup is 70% of its original
price. You want to buy Meinz' ketchup with an original price of $8.90.
What is the sale price?

Answers

Answer: $2.67

Step-by-step explanation:

$8.90 - $6.23 = $2.67

Brainliest? Im just trying to get to a higher rank

Which any quality represents the statement the sum of -3 and a number is at least 5

Answers

5 is less than or equal to -3+x

Answer: -3 + n >= 5

Step-by-step explanation: I got it wrong on the test but got the correct answer from test review on K12

Alyssa needs 4 pieces of wood that are 12 inches long to build a box. She bought a length of wood that was 60 inches long. How much extra wood does she have?

Answers

Answer:

She has 12 inches wood left

Step-by-step explanation:

Pls help plz thank you

Answers

Answer:

14, 31, 62

Step-by-step explanation:

11 + 3 = 14

14*2 = 28

28 + 3 = 31

31*2=62

Jaxon Rollison
10 of 1410 of 14 Items









Question
A salesperson earns $8 per hour plus 6% commission on her sales. In a week when she worked 40 hours, her total earnings were $692.

What was the total amount of her sales for the week?

Answers

Answer:

6200

Step-by-step explanation:

first find how much she would make purely based on hours worked:

8x40 = 320 dollars

next subtract this from total on her paycheck so 692-320 is 372

we know that 372 is 6% of a number so...

[tex]\frac{6}{100}[/tex] x = 372

[tex]\frac{6x}{100}[/tex] = 372

6x= 37200(100)

x=6200 $ divide by 6

so she sold $6200 worth of merchandise to earn $372 of commission

22. PLEASE HELP PLEASSSSSSEEEEEEEE

Answers

Answer:

me too i need help its in my HW and exam

Step-by-step explanation:

this is long division… please help

Answers

Answer:

23.35

Step-by-step explanation:

b) How fast should a boy of 40kg mass run so that the kinetic energy becomes 800J? ​

Answers

Answer:

v = 6.32  m/s

Step-by-step explanation:

Given Data:

Mass = m = 40 kg

Kinetic Energy = KE = 800 J

Required:

Speed = v = ?

Formula:

[tex]\displaystyle KE = \frac{1}{2} mv^2[/tex]

Solution:

Rearrange the formula for speed

[tex]\displaystyle v =\sqrt{\frac{2KE}{m} } \\\\Put \ values\\\\v = \sqrt{\frac{2(800)}{40} } \\\\v = \sqrt{2(20) } \\\\v = \sqrt{40} \\\\\boxed{v = 6.32 \ m/s}\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

how do you find the value of x on this triangle?

Answers

Answer:

Solving for X in a Right Triangle

Step-by-step explanation:

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

4. Prove or disprove the following statement: Given two numbers, increasing both numbers by 10% results in two numbers whose difference is the same as the difference of the two original numbers. Give a numerical example and explain.​

Answers

Step-by-step explanation:

increase by 10% is the same as multiplying by 1.1.

so, we get the assumption that

x - y = 1.1x - 1.1y = 1.1(x - y)

for the case that x <> y, now we can divide both sides by (x - y) and get

1 = 1.1

and that is wrong in all cases.

so, it is disproven for all x <> y.

for x = y the statement is true, the difference is in both cases 0.

e.g.

100 and 200

the difference is 100

100+10% = 110

200+10% = 220

and the difference is 110 (different to the original 100).

but 100 and 100, sure, the difference is 0, and the difference between 110 and 110 is still 0.

adding a % to a number means the size of the added part depends on the size of the basic number. the same % of a larger number is larger than the same % of a smaller number. therefore, the distance grows.

Which of the following statements explains the correct method to solve the equation 7x - 8 = 48?

Answers

Answer:

Follow the explanation below.

Step-by-step explanation:

7x = 48 - 8

7x = 40

x = 40/7

x = 5.714

List all the factors of 19. Tell whether 19 is prime or composite.

Answers

Answer:

19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)

Step-by-step explanation:

A car can travel 300 miles on 12 gallons of gas. At this rate, how many miles can the car travel on 1 gallon of gas?


12 miles

12 miles

25 miles

25 miles

120 miles

120 miles

312 miles

312 miles

Answers

Answer:

25 miles?

Step-by-step explanation:

HELLLP PLSSS QUICK



29 + 9x ≤ 65
solve for x

Answers

Answer:

x <= 4

Step-by-step explanation:

29+9x<65

-29.      -29

9x<36

divide both sides by 9

x less than or equal to 4

Answer:

x ≤ 4

Step-by-step explanation:

29 + 9x ≤ 65

subtract 29 from both sides

29 - 29 + 9x ≤ 65 - 29

9x ≤ 36

divide both sides by 9

9x / 9 = x and 36 / 9 = 4

we're left with x ≤ 4

Nolan had 30 minutes to do a three-problem quiz. He spent 8 7/10 minutes on question A and 4 2/5 minutes on question B. How much time did he have left for question C?

Answers

Answer:

16 9/10 minutes

Step-by-step explanation:

She is solving 3 questions, so her total time spent =

Total time = Time spent on A + Time spent on B + Time spent on C

30 minutes = 8 7/10 + 4 2/5 + Time C

Time C = 30 minutes - (8 7/10 + 4 2/5)minutes

Time C = 30 minutes - (13 1/0 minutes)

Time C = 16 9/10 minutes

Answer: 16m 54s

Step-by-step explanation:

8 7/10 + 4 2/5 = 13 1/10 or 13m 6s

30m - 13m 6s = 16m 54s

Could i have Brainliest, I am trying to rank up

HELPPPPP please its worth 50

Answers

[tex](3 {m}^{6} {n}^{2} ) ^{3} .2m {n}^{4} \\ = {3}^{3} {m}^{6 \times 3} {n}^{2 \times 3} \times 2 m{n}^{4} \\ = 27 {m}^{18} {n}^{6} \times 2m {n}^{4} \\ = (27 \times 2) {m}^{18 + 1} {n}^{6 + 4} \\ = 54 {m}^{19} {n}^{10} [/tex]

Answer:

[tex]54 {m}^{19} {n}^{10} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Solution given:

[tex]\bold{(3m^6n²)³.2mn⁴}[/tex]

distribute power

[tex]3³m^{6*3}n^{2*3}.2mn⁴[/tex]

[tex]27m^{18}n^6.2mn⁴[/tex]

multiply like terms and add or subtract power in multiplication

[tex]27*2.m^{18+1}n^{6+4}[/tex]

[tex]\large{\bold{54m^{18}n^{10}}}[/tex] is a required answer

PLZ SOLVE THE PROBLEM

Answers

Answer:

[tex]-2\frac{1}{2}[/tex]

Step-by-step explanation:

→ Minus the 2 numbers from each other

[tex]-1\frac{1}{5} -1\frac{3}{10}[/tex]

→ Find the LCM

[tex]-1\frac{2}{10} -1\frac{3}{10}[/tex]

→ Simplify

[tex]-2\frac{5}{10} =-2\frac{1}{2}[/tex]

Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100

6.0 • 25 = x

Answers

The equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100

Percentages can be expressed as decimals or fractions.

Given the expression 60% of 25, this can b expressed as:

60% of 25 = x

where x is the result of the expression.

60/100 * 25 = x

Expressing 60% as a decimal will give;

0.6 of 25  = x

0.6 * 25 = x

From the expression 60/100 * 25 = x, this can also be written as:

25 = 100/60 x

25 = 10/6 x

25 = 1.6x

Hence the equation which is equivalent to 60% of 25 are x • 1.6 = 25, 0.6 • 25 = x and x/25=60//100

Learn more on equation here: https://brainly.com/question/2972832

Evaluate 7+4b when b= 3

Answers

Answer:

19

Step-by-step explanation:

7+ 4(3)

7+12= 19

Mark me brainliest!!

What is -27/8×7/10
Because odbeoqhqbebebsns

Answers

The answer to this problem is going to be -2.3625

3 movie tickets cost 3690$. At this rate, the cost per ticket is $....

Answers

Answer: The cost per ticket is $1,230.

Explanation: 3,690/3 = 1,230.

Answer: The cost for each ticket is $1,230.

Step-by-step explanation:

Which equation below compares the amount of medicine, S, in Sofia’s system with the amount of medicine, L, in Lexi’s system? L = 16 x S S = 16 x L L = 4 + S S = 4 + L

Answers

Answer:

L=16xS

Step-by-step explanation:

A square plywood platform has a perimeter which is 11 times the length of a side,
decreased by 42. Find the length of a side. (P = 4L)

Answers

Answer:

Step-by-step explanation:

Assume that the demand curve D(p) given below is the market demand for widgets:

Q=D(p)=1204−11p, p > 0

Let the market supply of widgets be given by:

Q=S(p)=−3+6p, p > 0

where p is the price and Q is the quantity. The functions D(p) and S(p) give the number of widgets demanded and supplied at a given price.

What is the equilibrium price?
Please round your answer to the nearest hundredth.

What is the equilibrium quantity?
Please round your answer to the nearest integer.

What is the consumer surplus at equilibrium?
Please round the intercept to the nearest tenth and round your answer to the nearest integer

What is the producer surplus at equilibrium?
Please round the intercept to the nearest tenth and round your answer to the nearest integer.

What is the unmet demand at equilibrium?
Please round your answer to the nearest integer.

Answers

Answer:

Step-by-step explanation:

I'll use y for quantity and x for price [love my x and y] and rewrite the demand and supply functions:

Demand:    y=1204−11x

Supply:       y = -3 + 6x

==

We want to know the equilibrium price and quantity.  The quantities purchased and sold would be equal to the quantities supplied:

  1204−11x = -3 + 6x

-17x = - 1207

 x = 71  The price of a widget is 71 units ($, €,£,¥, etc.) at equilibrium

A price of 71 would lead to a demand and supply of:

y = 1204−11x

y = 1204−11(71)

y = 423 Widgets

We can also plot this to find the point (71,423).  See the attachment.

At this point, I'm uncertain how to answer the "producer surplus" and "unmet demand" at equilibrium.  This is what I did, so please judge if it is correct.

The demand line, y=1204−11x, tells us that if the price were 0, the demand would be 1204, which I'll assume in the maximum, since it is stipulated that x > 0  (I imagine it may no longer be a straight line when the price goes into negative territory.  I'd be the first in line to accept a widget and $5 if they were priced at -$5).

At equilibrium, therefore, we would still have an unmet demand of (1204 - 423) or 781 widgets that customers wanted, but wouldn't pay the price.

It seems to me that this would also be the unmet demand:  Product that could have been sold, but wasn't, due to the price.  I'm unsure, however.

Why is cube root of 9 equal to 9 to the one third power question mark

Answers

Answer:

3

just because

Answer:

See below

Step-by-step explanation:

[tex]\sqrt[3]{9}=9^{\frac{1}{3}}[/tex]

[tex](\sqrt[3]{9})^3=(9^{\frac{1}{3}})^3[/tex]

[tex]9=9^{\frac{1}{3}*3[/tex]

[tex]9=9^\frac{3}{3}[/tex]

[tex]9=9^1[/tex]

[tex]9=9[/tex]

Remember that [tex](a^b)^c=a^{b*c}[/tex]

please help me out y'all ​

Answers

first graph= negative association

second graph = no association

third graph = positive association

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