Question

manuela solved the equation $3 - 2|0.5x + 1.5| = 2$ for one solution. her work is shown below.
$3 - 2|0.5x + 1.5| = 2$
$-2|0.5x + 1.5| = -1$
$|0.5x + 1.5| = 0.5$
$0.5x + 1.5 = 0.5$
$0.5x = -1$
$x = -2$
what is the other solution to the equation?
$\bigcirc$ $x = -6$
$\bigcirc$ $x = -4$
$\bigcirc$ $x = 2$
$\bigcirc$ $x = 4$

Explanation:

Step1: Recall absolute value property

For \(|A| = B\) (\(B\geq0\)), \(A = B\) or \(A=-B\). We have \(|0.5x + 1.5|=0.5\), so the other case is \(0.5x+1.5=- 0.5\).

Step2: Solve for \(x\)

Subtract \(1.5\) from both sides: \(0.5x=-0.5 - 1.5\)
Simplify right - hand side: \(0.5x=-2\)
Divide both sides by \(0.5\): \(x=\frac{-2}{0.5}=-4\)

Answer:

\(x = - 4\) (corresponding to the option "x=-4")