Question

solve the absolute value equation $13 - 4|15 + 3x| + 3 = 16$. (1 point)
the solution to the absolute value equation is $x = \square$.

Explanation:

Step1: Simplify the equation

First, combine the constant terms on the left side. \(13 + 3 = 16\), so the equation becomes \(16 - 4|15 + 3x| = 16\).

Step2: Isolate the absolute value term

Subtract 16 from both sides: \(-4|15 + 3x| = 16 - 16 = 0\). Then divide both sides by -4: \(|15 + 3x| = \frac{0}{-4} = 0\).

Step3: Solve for x

Since the absolute value of a number is 0 only when the number itself is 0, we set \(15 + 3x = 0\). Subtract 15 from both sides: \(3x = -15\). Divide both sides by 3: \(x = \frac{-15}{3} = -5\).

Answer:

\(x = -5\)