Question

2x + |3x-8| = - 4. Help me to solve this problem about equation please?

Answer 1

no solutions

Explanation:

Given: `2x + |3x-8| = -4`

An absolute value always yields a positive answer.

This problem could have up to two solutions since there are two equations:

`2x + 3x -8 = -4 " or " 2x +(-(3x - 8)) = -4`

Distribute the negative in the 2nd equation:

`2x + 3x -8 = -4 " or " 2x -3x + 8 = -4`

Add/subtract like terms on the left side:

`5x - 8 = 4 " or " -x + 8 = -4`

Add/subtract the constant to the right side:

`5x = 4 " or " -x = -12`

Divide as needed to isolate the variable:

`x = 4/5, " " x = 12`

ALWAYS CHECK Answers for absolute value functions:

1st solution:
`2/1 * 4/5 + |3/1 * 4/5 - 8/1 * 5/5| = -4`

`8/5 + |12/5 - 40/5| = -4`

`8/5 + |-28/5| = -4`

`8/5 + 28/5 = 36/5 != -4" " x = 4/5` is NOT a solution

2nd solution:
`2 * 12 + |3*12 - 8| = -4`

`24 + |36 - 8| = -4`

`24 + 28 = 52 != -4" "x = 12` is NOT a solution