# How do you solve 3/4abs(y+2)=6?

Mar 26, 2018

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}}$ to isolate the absolute value function while keeping the equation balanced:

$\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times \frac{3}{4} \left\mid y + 2 \right\mid = \frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times 6$

$\frac{12}{12} \left\mid y + 2 \right\mid = \frac{24}{\textcolor{b l u e}{3}}$

$1 \left\mid y + 2 \right\mid = 8$

$\left\mid y + 2 \right\mid = 8$

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

$y + 2 = - 8$

$y + 2 - \textcolor{red}{2} = - 8 - \textcolor{red}{2}$

$y + 0 = - 10$

$y = - 10$

Solution 2:

$y + 2 = 8$

$y + 2 - \textcolor{red}{2} = 8 - \textcolor{red}{2}$

$y + 0 = 6$

$y = 6$

The Solution Set Is:

$x = \left\{- 10 , 6\right\}$

Mar 26, 2018

$y = - 10 , 6$

#### Explanation:

Because you don't know if y is positive or negative, $| y + 2 |$ equals both $\left(y + 2\right)$ and $- \left(y + 2\right)$

Start by dividing both sides by $\frac{3}{4}$:

$| y + 2 | = 6 \left(\frac{4}{3}\right)$

$| y + 2 | = 8$

Then set up two equations and solve:

$y + 2 = 8$

$y = 6$

and

$- \left(y + 2\right) = 8$

$- y - 2 = 8$

$- y = 10$

Multiply both sides by $- 1$

$- y \times - 1 = 10 \times - 1$

$y = - 10$