# How do you solve abs(3+4x)<=15?

Mar 10, 2017

See the entire solution process below:

#### Explanation:

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. Therefore we need to write this problem as a system of inequalities:

$- 15 \le 3 + 4 x \le 15$

Next, subtract $\textcolor{red}{3}$ from each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- \textcolor{red}{3} - 15 \le - \textcolor{red}{3} + 3 + 4 x \le - \textcolor{red}{3} + 15$

$- 18 \le 0 + 4 x \le 12$

$- 18 \le 4 x \le 12$

Now, divide each segment of the system by $\textcolor{red}{4}$ to solve for $x$ while keeping the system balanced:

$- \frac{18}{\textcolor{red}{4}} \le \frac{4 x}{\textcolor{red}{4}} \le \frac{12}{\textcolor{red}{4}}$

$- \frac{9}{2} \le \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} \le 3$

-9/2 <= x <= 3#