Question

For each equation below, solve for x. Check your solution, if possible, and show all work. a. 3x - 6 + 1 = -2x - 5 + 5x b. -2x - 5 = 2 - 4x - (x - 1)

Answer 1

A: x = all real numbers

B: x = 8/3

Explanation:

Part A:

`3x-6+1=-2x-5+5x`

Combine like terms:

`3x-5=-5+3x`

Add 5 to both sides:

`3x=3x`

Divide each side by 3x:

`1=1`

All real numbers are valid solutions.

Part B:

`-2x - 5 = 2 - 4x - (x - 1)`

Distribute the negative in front of the parenthesis:

`-2x - 5 = 2 - 4x -x+1`

Combine like terms:

`-2x - 5 = 3 -5x`

Add 5x to each side:

`3x - 5 = 3`

Add 5 to each side:

`3x=8`

Divide each side by 3:

`(8)/(3) =x`