# How do you solve 7-3abs(4d-7)=4?

Aug 2, 2015

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

#### Explanation:

Your absolute value equation looks like this

$7 - 3 | 4 d - 7 | = 4$

Start by isolating the modulus on one side of the equation

$\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} - 3 | 4 d - 7 | = 4 - 7$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} \cdot | 4 d - 7 |}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}}} = \frac{- 3}{- 3}$

$| 4 d - 7 | = 1$

Now, this equation will produce two values for $d$, depending on which condition is true

• If $\left(4 d - 7\right) > 0$, then you have

$| 4 d - 7 | = 4 d - 7$

and the equation becomes

$4 d - 7 = 1 \implies d = \frac{8}{4} = \textcolor{g r e e n}{2}$

• If $\left(4 d - 7\right) < 0$, then you have

$| 4 d - 7 | = - \left(4 d - 7\right) = - 4 d + 7$

This will get you

$- 4 d + 7 = 1 \implies d = \frac{6}{4} = \textcolor{g r e e n}{\frac{3}{2}}$