# How do you solve 0.7(2m-5)>=21.7?

Oct 17, 2016

$m \ge 18$

#### Explanation:

Treat an inequality in the same way as an equation unless you multiply or divide by a negative, which does not apply in this case.

We could start by multiplying $0.7$ into the bracket, but we eventually want the $m$ on its own, so rather start by dividing both sides by $0.7$

$\frac{0.7}{0.7} \left(2 m - 5\right) \ge \textcolor{red}{\frac{21.7}{0.7}}$

[Recall: dividing by a decimal:$\textcolor{red}{\frac{21.7}{0.7} = \frac{21.7 \times 10}{0.7 \times 10} = \frac{217}{7}}$]

$2 m - 5 \ge \textcolor{red}{\frac{217}{7}} \text{ } \leftarrow + 5$ to both sides

$2 m \ge 31 + 5$

$2 m \ge 36$

$m \ge 18$