manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. her work is shown below. 3 - 2|0.5x +…

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? x = - 6 x = - 4 x = 2 x = 4

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? x = - 6 x = - 4 x = 2 x = 4

Answer

Answer:

A. $x = - 4$

Explanation:

Step1: Recall absolute - value property

For $|a| = b$ ($b\geq0$), $a = b$ or $a=-b$. We have $|0.5x + 1.5|=0.5$.

Step2: Consider the negative case

Set $0.5x+1.5=-0.5$.

Step3: Solve for $x$

Subtract $1.5$ from both sides: $0.5x=-0.5 - 1.5$. So $0.5x=-2$.

Step4: Isolate $x$

Divide both sides by $0.5$: $x=\frac{-2}{0.5}=-4$.