# How do you solve and write the following in interval notation: x/2 + 3 ≤ 1?

Sep 3, 2017

See a solution process below:

#### Explanation:

This is a standard 2-Step problem:

Step 1: Isolate The Variable: Subtract $\textcolor{red}{3}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$\frac{x}{2} + 3 - \textcolor{red}{3} \le 1 - \textcolor{red}{3}$

$\frac{x}{2} + 0 \le - 2$

$\frac{x}{2} \le - 2$

Step 2: Multiply or Divide by the Appropriate Term to Solve for the Variable: Multiply each side of the inequality by $\textcolor{red}{2}$ to solve for $x$ while keeping the inequality balanced:

$\textcolor{red}{2} \times \frac{x}{2} \le \textcolor{red}{2} \times - 2$

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

$x \le - 4$

Or, in interval notation:

$\left(- \infty , - 4\right]$