Question

How do you solve `abs(9p+6)=3`?

Answer 1

`p` can equal `-1/3` or `-1`.

Explanation:

An absolute value, indicated by `||`, means that you use the number's distance from zero. In other words, the number becomes positive. For example, `|-1|` and `|1|` both equal `1`, because both are `1` away from zero.

Both the negative and positive forms of a number equal the same thing in absolute value form. This means that `3=9p+6` or `3=-(9p+6)`.

To find the answer, we must solve both equations.

First, `3=9p+6`. We need to isolate the variable and then simplify.

`3-6=9p`
`-3=9p`
`-3/9=p`
`-1/3=p`

Next, `3=-(9p+6)`. We must distribute the negative, and then isolate and simplify.

`3=-9p-6`
`3+6=-9p`
`9=-9p`
`9/-9=p`
`-1=p`

Therefore, `p` can equal `-1/3` or `-1`.

Answer 2

`p=-1,-1/3`

Explanation:

Solve:

`abs(9p+6)=3`

Since `absa=a` and `abs(-a)=a`, we can break the given equation into two equations:

`9p+6=3` and `-(9p+6)=3`

Solve the first equation.

`9p+6=3`

Subtract `6` from both sides.

`9p+6-6=3-6`

`9p=-3`

Divide both sides by `9`.

`p=-3/9`

Simplify.

`p=-1/3`

Solve the second equation.

`-(9p+6)=3`

Expand.

`-9p-6=3`

Add `6` to both sides.

`-9p-6+6=3+6`

`-9p=9`

Divide both sides by `-9`.

`p=-9/9`

Simplify.

`p=-1`

`p=-1,-1/3`