How do you solve abs(4y+5)=7?

Dec 21, 2016

$y = \frac{1}{2}$ and $y = - 3$

Explanation:

Because the absolute value function transform positive or negative number into a positive number we need to solve the interior of the absolute value function for both the negative and positive form of its equality:

Solution 1)

$4 y + 5 = \textcolor{b l u e}{7}$

$4 y + 5 - \textcolor{red}{5} = 7 - \textcolor{red}{5}$

$4 y + 0 = 2$

$4 y = 2$

$\frac{4 y}{\textcolor{red}{4}} = \frac{2}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} = \frac{1}{2}$

$y = \frac{1}{2}$

Solution 2)

$4 y + 5 = \textcolor{b l u e}{- 7}$

$4 y + 5 - \textcolor{red}{5} = - 7 - \textcolor{red}{5}$

$4 y + 0 = - 12$

$4 y = - 12$

$\frac{4 y}{\textcolor{red}{4}} = - \frac{12}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} = - 3$

$y = - 3$