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

May 16, 2015

To solve for $d$ we look at both ends of the absolute where it will equal either $5$ or $- 5$ so this is what we do.

$\left\mid 4 d + 7 \right\mid = 5$

can be re written as

$4 d + 7 = 5$ or $4 d + 7 = - 5$

$4 d = - 2$ or $4 d = - 12$

$d = - \frac{1}{2}$ or $d = - 3$

keep in mind that the absolute sign means that what ever is inside the "Brackets" of the absolute, will always be positive, thus if the result inside is $\left\mid - 5 \right\mid$ it will equal $5$ ...

to rewrite $\left\mid - 5 \right\mid = 5$