Question

Solve each of the following equations. Show its solution set on a number line. Check your answers.

|4x−4(x+1)|=4

Answer 1

Explanation:

Step 1: Distribute

`|4x-4(x+1)|=4`

`|4x - (4 * x) - (4 * 1)| = 4`

`|4x - 4x - 4| = 4`

`|-4| = 4`

`4 = 4`

Answer: All real numbers

Check, pick x = 2

`|4(2) - 4(2 + 1)| = 4`

`|8 - (4 * 2) - (4 * 1)| = 4`

`|8 - 8 - 4| = 4`

`|-4| = 4`

`4 = 4`

True

Answer 2

see below

Explanation:

|4x−4(x+1)|=4

First simplify in the absolute value

Distribute

|4x−4x-4|=4

|-4|=4

Taking the absolute value

4 =4

This is always true

X is all real numbers

Pick any value for x and it will be a true statement

x=0

|4*0−4(*0+1)|=4

|-4|=4

Let x = 5

|4*5−4(5+1)|=4

|20−24|=4

|−4|=4