Question

Solve the absolute value equation
13
−
4
|
15
+
3
x
|
+
3
=
16
.(1 point)


The solution to the absolute value equation is
x

=

Answer 1

To solve the absolute value equation

\[
13 - 4 |15 + 3x| + 3 = 16,
\]

we first simplify the left side:

\[
13 + 3 - 4 |15 + 3x| = 16,
\]

which simplifies to

\[
16 - 4 |15 + 3x| = 16.
\]

Next, we subtract 16 from both sides:

\[
-4 |15 + 3x| = 0.
\]

Dividing by -4, we find:

\[
|15 + 3x| = 0.
\]

The absolute value of an expression is zero only when the expression itself is zero. Thus, we set the inside of the absolute value to zero:

\[
15 + 3x = 0.
\]

Solving for \(x\), we subtract 15 from both sides:

\[
3x = -15,
\]

and then divide by 3:

\[
x = -5.
\]

Thus, the solution to the absolute value equation is

\[
\boxed{-5}.
\]