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

b

Explanation:

just took the quiz and got it right :))

Answer 2

x=-4

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.

`(-2|0.5x+1.5|)/(-2)=(-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.