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9. What is the solution set of the equation below?
3|5- X| + 2 = 29

9. What is the solution set of the equation below? 3|5- X| + 2 = 29-example-1
User Kandinski
by
4.3k points

1 Answer

3 votes

Answer:

x=−4

x=14

Explanation:

Absolute Value Equation entered :

3|5-x|+2=29

Step by step solution :

STEP

1

:

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

3|-x+5|+2 = 29

Another term is moved / added to the right hand side.

3|-x+5| = 27

STEP

2

:

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is 3|-x+5|

For the Negative case we'll use -3(-x+5)

For the Positive case we'll use 3(-x+5)

STEP

3

:

Solve the Negative Case

-3(-x+5) = 27

Multiply

3x-15 = 27

Rearrange and Add up

3x = 42

Divide both sides by 3

x = 14

STEP

4

:

Solve the Positive Case

3(-x+5) = 27

Multiply

-3x+15 = 27

Rearrange and Add up

-3x = 12

Divide both sides by 3

-x = 4

Multiply both sides by (-1)

x = -4

Which is the solution for the Positive Case

STEP

5

:

Wrap up the solution

x=14

x=-4

Solutions on the Number Line

Two solutions were found :

x=-4

x=14

User Nikhil Seepana
by
3.7k points