# How do you solve abs(2y+7)=7?

Jul 20, 2017

As the absolute value of $2 y + 7 = 7$, then $2 y + 7 = \pm 7$, as abs(), takes the magnitude of the number, whether its positive or negative, abs(), makes it positive.

So, either $2 y + 7 = 7$, or $2 y + 7 = - 7$

Let's solve $2 y + 7 = 7$ first:
We take 7 from both sides first- $2 y + 7 - \textcolor{red}{7} = 7 - \textcolor{red}{7} \equiv 2 y = 0$

Then we divide both sides by 2 - $\frac{2 y}{\textcolor{red}{2}} = \frac{0}{\textcolor{red}{2}} \equiv y = 0$

Now, let's solve for $2 y + 7 = - 7$:
We take 7 from both sides first- $2 y + 7 - \textcolor{red}{7} = - 7 - \textcolor{red}{7} \equiv 2 y = - 14$

Then we divide both sides by 2 - $\frac{2 y}{\textcolor{red}{2}} = - \frac{14}{\textcolor{red}{2}} \equiv y = - 7$