Question

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


The solution to the absolute value equation is x =

Answer 1

To solve the equation \( 13 - 4|15 + 3x| + 3 = 16 \), we first simplify the equation.

Combine the constants on the left side:

\[
13 + 3 = 16
\]

So, the equation simplifies to:

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

Next, we subtract 16 from both sides:

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

Now, we divide by -4:

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

Since the absolute value is equal to 0, this means:

\[
15 + 3x = 0
\]

Now, we solve for \( x \):

\[
3x = -15
\]
\[
x = -5
\]

Thus, the solution to the absolute value equation is:

\[
\boxed{-5}
\]