Question

Solve this absolute value equation and show all work.

1) 9 + |2x - 3| = 7

2) 3 + |2x - 4| = 15

Answer 1

For the equation

1)
`9 + | 2x - 3 | = 7`

x=0.5 and x=2.5

For the equation

2)
`3 + | 2x - 4 | = 15`

x=8 and x=-4

Explanation:

For the equation

1)
`9 + | 2x - 3 | = 7`

we have 2 cases

Case 1
`(2x - 3)> 0`

`9 + 2x - 3 = 7\\2x = 7 + 3-9\\2x = 1\\x = 0.5`

Case 2
`(2x - 3) <0`

`9 - (2x - 3) = 7\\-2x + 3 = 7-9\\-2x = 7-9-3\\-2x = -5\\x = 2.5`

For the equation

2)
`3 + | 2x - 4 | = 15`

we have 2 cases

Case 1
`(2x - 4)> 0`

`3 + 2x - 4 = 15\\2x = 15 + 4-3\\2x = 16\\x = 8`

Case 2
`(2x - 4) <0`

`3 - (2x - 4) = 15\\-2x +4 = 15-3\\-2x = 15-3-4\\-2x = 8\\x = -4\\`