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?

x=−6
x=−4
x=2
x=4

Answer 1

Absolute value gives two cases. From |0.5x+1.5| = 0.5 we have

0.5x+1.5 = 0.5 -> x = −2 (Manuela's solution),
or 0.5x+1.5 = −0.5 -> 0.5x = −2 -> x = −4.

So the other solution is x = −4.