Question

Solve. |3(x + 1) - 5| = -2x + 7 A) x = 9 5 B) x = -5 and 9 5 C) x = 9 5 and 5 D) x = 9 5 and 9 E) x = - 9 5 and 9

Answer 1

`x = (9)/(5)` and x = -5

So the correct answer is letter B

Explanation:

It is quite helpful to start this kind of problem from a simple example.

|a| = b is if a = b or if a = -b. |x| = 2 if x = 2 or if x = -2.

So in your question, we have:

a = 3(x + 1) - 5

b = -2x + 7

Applying like we saw in the bolded line, there are two solutions

Solution 1: |a| = b if a = b

a = b

3(x + 1) - 5 = -2x + 7

3x + 3 -5 = -2x + 7

3x - 2 = -2x + 7

3x + 2x = 7 + 2

5x = 9

`x = (9)/(5)`

Solution 2: |a| = b if a = -b

a = -b

3(x + 1) - 5 = -(-2x + 7)

3x + 3 -5 = 2x - 7

3x - 2 = 2x - 7

3x - 2x = -7 + 2

x = -5