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?

Answer 1

Answer:

x=-4

Step-by-step explanation:

The given equation is

$3-2|0.5x+1.5|=2$

Subtract 3 from both sides.

$3-2|0.5x+1.5|-3=2-3$

$-2|0.5x+1.5|=-1$

Divide both sides by -2.

$\dfrac{-2|0.5x+1.5|}{-2}=\dfrac{-1}{-2}$

$|0.5x+1.5|=0.5$

If |x|=a, then x=a or x=-a.

$0.5x+1.5=\pm 0.5$

Case 1: $0.5x+1.5=0.5$

Subtract 1.5 from both sides.

$0.5x=0.5-1.5$

$0.5x=-1$

Divide both sides by 0.5.

$x=-2$

Case 2: $0.5x+1.5=-0.5$

Subtract 1.5 from both sides.

$0.5x=-0.5-1.5$

$0.5x=-2$

Divide both sides by 0.5.

$x=-4$

Therefore, one solution is x=-2 and other solution is x=-4.

Answer 2

Answer:

b

Step-by-step explanation:

just took the quiz and got it right :))