# How do you solve -2r<(6-2r)/5 and graph the solution on a number line?

Mar 17, 2017

$r > - \frac{3}{4}$

An open circle on $- \frac{3}{4}$ and a line drawn to the right.

#### Explanation:

Treat inequalities in exactly the same way as an equation, but you may not cross-multiply.

If you multiply or divide by a negative value, the inequality sign changes around.

$- 2 r < \frac{6 - 2 r}{5} \text{ } \times 5$

$- 2 r \textcolor{red}{\times 5} < \frac{\left(6 - 2 r\right) \textcolor{red}{\times 5}}{5}$

$- 10 r < 6 - 2 r \text{ }$re-arrange the terms to make $r$ positive

$- 6 < - 2 r + 10 r$

$- 6 < 8 r \text{ } \div 8$

$- \frac{6}{8} < r$

$r > - \frac{3}{4}$

On the number line this will shown as an open circle on $- \frac{3}{4}$ because it is NOT included as part of the solution, and a line drawn to the right.