# How do you solve and graph 3/4j-10>=5?

Jul 30, 2017

See a solution process below:

#### Explanation:

Step 1) Add $\textcolor{red}{10}$ to each side of the inequality to isolate the $j$ term while keeping the inequality balanced:

$\frac{3}{4} j - 10 + \textcolor{red}{10} \ge 5 + \textcolor{red}{10}$

$\frac{3}{4} j - 0 \ge 15$

$\frac{3}{4} j \ge 15$

Step 2) Multiply each side of the inequality by $\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}}$ to solve for $j$ while keeping the inequality balanced:

$\frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times \frac{3}{4} j \ge \frac{\textcolor{red}{4}}{\textcolor{b l u e}{3}} \times 15$

$\frac{\cancel{\textcolor{red}{4}}}{\cancel{\textcolor{b l u e}{3}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} j \ge \frac{\textcolor{red}{4}}{\cancel{\textcolor{b l u e}{3}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{15}}} 5$

$j \ge 20$

We can graph this solution as:

graph{x >= 20 [-30, 30, -10, 10]}