Question

Solve |4x+8−1|=15
.(2 points)
The solutions are x=

and x=

Answer 1

To solve the equation \( |4x + 8 - 1| = 15 \), we first simplify the expression inside the absolute value:

\[
4x + 8 - 1 = 4x + 7
\]

So, the equation becomes:

\[
|4x + 7| = 15
\]

This absolute value equation can be split into two separate cases:

1. \( 4x + 7 = 15 \)
2. \( 4x + 7 = -15 \)

**Case 1:**

\[
4x + 7 = 15
\]

Subtract 7 from both sides:

\[
4x = 15 - 7
\]

\[
4x = 8
\]

Now divide by 4:

\[
x = 2
\]

**Case 2:**

\[
4x + 7 = -15
\]

Subtract 7 from both sides:

\[
4x = -15 - 7
\]

\[
4x = -22
\]

Now divide by 4:

\[
x = -\frac{22}{4} = -\frac{11}{2}
\]

Thus, the solutions are:

\[
x = 2 \quad \text{and} \quad x = -\frac{11}{2}
\]

To summarize, the solutions are:

\[
x = 2 \quad \text{and} \quad x = -\frac{11}{2}
\]