Question

Solve the equation.
5|x+5| =16

Answer 1

To solve the equation \(5|x + 5| = 16\), we can first isolate the absolute value term by dividing both sides by 5:

\[
|x + 5| = \frac{16}{5}
\]

Now we need to solve the equation \( |x + 5| = \frac{16}{5} \). This gives us two cases to consider:

**Case 1**: \(x + 5 = \frac{16}{5}\)

Subtracting 5 from both sides, we have:

\[
x = \frac{16}{5} - 5 = \frac{16}{5} - \frac{25}{5} = \frac{16 - 25}{5} = \frac{-9}{5}
\]

**Case 2**: \(x + 5 = -\frac{16}{5}\)

Again, subtracting 5 from both sides:

\[
x = -\frac{16}{5} - 5 = -\frac{16}{5} - \frac{25}{5} = -\frac{16 + 25}{5} = -\frac{41}{5}
\]

Now we have two solutions:

\[
x = -\frac{9}{5} \quad \text{and} \quad x = -\frac{41}{5}
\]

Thus, the solutions to the equation \(5|x + 5| = 16\) are:

\[
\boxed{-\frac{9}{5}} \quad \text{and} \quad \boxed{-\frac{41}{5}}
\]