How do you solve |-4x + 5| + 3 = 30?

Oct 16, 2017

See a solution process below:

Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the absolute value function while keeping the equation balanced:

$\left\mid - 4 x + 5 \right\mid + 3 - \textcolor{red}{3} = 30 - \textcolor{red}{3}$

$\left\mid - 4 x + 5 \right\mid + 0 = 27$

$\left\mid - 4 x + 5 \right\mid = 27$

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:

$- 4 x + 5 = - 27$

$- 4 x + 5 - \textcolor{red}{5} = - 27 - \textcolor{red}{5}$

$- 4 x + 0 = - 32$

$- 4 x = - 32$

$\frac{- 4 x}{\textcolor{red}{- 4}} = \frac{- 32}{\textcolor{red}{- 4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}} x}{\cancel{\textcolor{red}{- 4}}} = 8$

$x = 8$

Solution 2:

$- 4 x + 5 = 27$

$- 4 x + 5 - \textcolor{red}{5} = 27 - \textcolor{red}{5}$

$- 4 x + 0 = 22$

$- 4 x = 22$

$\frac{- 4 x}{\textcolor{red}{- 4}} = \frac{22}{\textcolor{red}{- 4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}} x}{\cancel{\textcolor{red}{- 4}}} = - \frac{22}{4}$

$x = - \frac{11}{2}$

The Solutions Are: $x = 8$ and $x = - \frac{11}{2}$