# How do you solve abs(x/7)=3?

Jun 12, 2017

$x = \pm 21$

#### Explanation:

Solve:

$\left\mid \frac{x}{7} \right\mid = 3$

$\left\mid a \right\mid = \pm a$ There are two equations to solve: one is positive, the other is negative.

Positive equation.

$\frac{x}{7} = 3$

Multiply both sides by $7$.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} = 3 \times 7$

$x = 21$

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Negative equation.

$- \frac{x}{7} = 3$

Multiply both sides by $7$.

$- x = 3 \times 7$

$- x = 21$

Divide both sides by $- 1$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{-}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{-}}} 1} = \frac{21}{- 1}$

$x = - 21$

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Solution:

$x = \pm 21$