Question

Solve for x: |2x+6| -4 = 20

a. x= 9 and x= 11
b. x= -9 and x=15
c. x=9 and x=-15
d. No solution

Answer 1

|2x + 6| - 4 = 20

First, add 4 to both sides. / Your problem should look like: |2x + 6| = 20 + 4
Second, simplify 20 + 4 to 24. / Your problem should look like: |2x + 6| = 24
Third, break down the problem into these 2 equations. / 2x + 6 = 24 and -(2x + 6) = 24
Fourth, solve the 1st equation: 2x + 6 = 24
Subtract 6 from both sides. / Your problem should look like: 2x = 24 - 6
Simplify 24 - 6 to 18. / Your problem should look like: 2x = 18
Divide both sides by 2. / Your problem should look like: x =
`(18)/(2)`
Simplify
`(18)/(2)` to 9 / Your problem should look like: x = 9
Fifth, solve the 2nd equation: -(2x + 6) = 24
Simplify brackets. / Your problem should look like: -2x - 6 = 24
Add 6 to both sides. / Your problem should look like: -2x = 24 + 6
Simplify 24 + 6 to 30. / Your problem should look like: -2x = 30
Divide both sides by -2. / Your problem should look like: x =
`(30)/(-2)`
Simplify
`(30)/(-2)` to
`- (30)/(2)` / Your problem should look like: x =
`-(30)/(2)`
Simplify
`(30)/(2)` to 15. / Your problem should look like: x = -15
Sixth, collect all of your solutions. / Your problem should look like: x = -15, 9

Answer: x = -15, 9 (C)