# How do you solve -9>=2/5m+7?

Apr 24, 2017

See the solution process below:

#### Explanation:

Step 1) Subtract $\textcolor{red}{7}$ from each side of the inequality to isolate the $m$ term while keeping the inequality balanced:

$- 9 - \textcolor{red}{7} \ge \frac{2}{5} m + 7 - \textcolor{red}{7}$

$- 16 \ge \frac{2}{5} m + 0$

$- 16 \ge \frac{2}{5} m$

Step 2) Multiply each side of the inequality by $\frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}}$ to solve for $m$ while keeping the inequality balanced:

$\frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}} \cdot - 16 \ge \frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}} \cdot \frac{2}{5} m$

$- \frac{80}{\textcolor{b l u e}{2}} \ge \frac{\cancel{\textcolor{red}{5}}}{\cancel{\textcolor{b l u e}{2}}} \cdot \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} m$

$- 40 \ge m$

To state the solution in terms of $m$ we can reverse or "flip" the entire inequality:

$m \le - 40$

Apr 24, 2017

Solution : $m \le - 40 \mathmr{and} \left(- \infty , - 40\right]$

#### Explanation:

$- 9 \ge \frac{2}{5} m + 7 \mathmr{and} - 9 - 7 \ge \frac{2}{5} m \mathmr{and} \frac{5}{2} \cdot \left(- 16\right) \ge m \mathmr{and} - 40 \ge m \mathmr{and} m \le - 40$
Solution : $m \le - 40 \mathmr{and} \left(- \infty , - 40\right]$ [Ans]