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 The other solution to the equation is.

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

diide 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