Question

savannah solved the equation 3 + 4|\frac{x}{2}+3| = 11 for one solution. her work is shown below: 1. 4|\frac{x}{2}+3| = 8 2. |\frac{x}{2}+3| = 2 3. \frac{x}{2}+3 = 2 4. \frac{x}{2}=-1 5. x=-2 what is the other solution to the given absolute - value equation? x =

Explanation:

Step1: Recall absolute - value property

For \(|a| = b\) (\(b\geq0\)), \(a = b\) or \(a=-b\). In step 2, we have \(|\frac{x}{2}+3| = 2\). We already considered \(\frac{x}{2}+3 = 2\) to get \(x=-2\). Now consider \(\frac{x}{2}+3=-2\).

Step2: Solve the new equation

Subtract 3 from both sides of \(\frac{x}{2}+3=-2\).
\(\frac{x}{2}=-2 - 3\)
\(\frac{x}{2}=-5\)

Step3: Isolate \(x\)

Multiply both sides by 2.
\(x=-10\)

Answer:

\(-10\)