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

X= -4

X=-2

Explanation:

for

|a|=b

assume

a=b and a=-b

so

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

minus 3 both sides

-2|0.5x+1.5|=-1

divide both sides by -2

|0.5x+1.5|=0.5

set negative and postivive

0.5x+1.5=0.5 and 0.5x+1.5=-0.5

solve each

0.5x+1.5=0.5

minus 1.5 both sides

0.5x=-1

times - 2 both sides

x=-2

other

0.5x+1.5=-0.5

minus 1.5 from oth sides

0.5x=-2

times 2 both sides

x=-4

the solutions are x=-2 and x=-4

Answer 2

x=-4

Explanation: