Question

2 l2x+7l = 16
Please help me with this ASAP

Answer 1

x = -
`(15)/(2)` , x =
`(1)/(2)`

Explanation:

2 | 2x + 7 | = 16 ( divide both sides by 2 )

| 2x + 7 | = 8

the absolute value function always gives a positive result, but the expression inside can be positive or negative , that is

2x + 7 = 8 ( subtract 7 from both sides )

2x = 1 ( divide both sides by 2 )

x =
`(1)/(2)`

or

- (2x + 7) = 8

- 2x - 7 = 8 ( add 7 to both sides )

- 2x = 15 ( divide both sides by - 2 )

x = -
`(15)/(2)`

As a check

substitute these values into the left side and if equal to the right side then they are a solution

x =
`(1)/(2)`

2 | 2(
`(1)/(2)` ) + 7 | = 2 | 1 + 7 | = 2 | 8 | = 16 = right side

x = -
`(15)/(2)`

2 | 2(-
`(15)/(2)` ) + 7 | = 2 | - 15 + 7 | = 2 | - 8 | = 2 | 8 | = 16 = right side

then x = -
`(15)/(2)` and x =
`(1)/(2)` are the solutions

Answer 2

x = 1/2 and

x = -15/2

Explanation:

First, get the absolute value alone on one side if the equation.

2 |2x + 7 | = 16

Divide both sides by 2.

| 2x + 7 | = 8

Once the absolute value sign is by itself, you will separate the equation into two separate equations.

2x+7=8 and 2x+7=-8

Solve these two equations separately and get two solutions.

2x + 7 = 8

Subtract 7.

2x = 1

Divide by 2.

x = 1/2 Here is one solution.

2x + 7 = -8

Subtract 7.

2x = -15

Divide by 2.

x = -15/2 Here is a second solution.