Question

Solve the absolute value equation for.

|5x+25|-90=40

Answer 1

To solve the equation \(|5x + 25| - 90 = 40\), we first isolate the absolute value expression.

1. Add 90 to both sides:
\[
|5x + 25| = 40 + 90
\]
\[
|5x + 25| = 130
\]

2. Now, we will split this into two cases based on the definition of absolute value.

### Case 1:
\[
5x + 25 = 130
\]
Subtract 25 from both sides:
\[
5x = 130 - 25
\]
\[
5x = 105
\]
Now divide by 5:
\[
x = \frac{105}{5}
\]
\[
x = 21
\]

### Case 2:
\[
5x + 25 = -130
\]
Subtract 25 from both sides:
\[
5x = -130 - 25
\]
\[
5x = -155
\]
Now divide by 5:
\[
x = \frac{-155}{5}
\]
\[
x = -31
\]

### Summary of Solutions
The solutions to the equation \(|5x + 25| - 90 = 40\) are:
\[
x = 21 \quad \text{and} \quad x = -31
\]

Thus, the final answer is:
\[
\boxed{21 \text{ and } -31}
\]