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

May 11, 2018

$p$ can equal $- \frac{1}{3}$ 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 $3 = 9 p + 6$ or $3 = - \left(9 p + 6\right)$.

To find the answer, we must solve both equations.

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

$3 - 6 = 9 p$
$- 3 = 9 p$
$- \frac{3}{9} = p$
$- \frac{1}{3} = p$

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

$3 = - 9 p - 6$
$3 + 6 = - 9 p$
$9 = - 9 p$
$\frac{9}{-} 9 = p$
$- 1 = p$

Therefore, $p$ can equal $- \frac{1}{3}$ or $- 1$.

May 11, 2018

$p = - 1 , - \frac{1}{3}$

#### Explanation:

Solve:

$\left\mid 9 p + 6 \right\mid = 3$

Since $\left\mid a \right\mid = a$ and $\left\mid - a \right\mid = a$, we can break the given equation into two equations:

$9 p + 6 = 3$ and $- \left(9 p + 6\right) = 3$

Solve the first equation.

$9 p + 6 = 3$

Subtract $6$ from both sides.

$9 p + 6 - 6 = 3 - 6$

$9 p = - 3$

Divide both sides by $9$.

$p = - \frac{3}{9}$

Simplify.

$p = - \frac{1}{3}$

Solve the second equation.

$- \left(9 p + 6\right) = 3$

Expand.

$- 9 p - 6 = 3$

Add $6$ to both sides.

$- 9 p - 6 + 6 = 3 + 6$

$- 9 p = 9$

Divide both sides by $- 9$.

$p = - \frac{9}{9}$

Simplify.

$p = - 1$

$p = - 1 , - \frac{1}{3}$