# How do you solve –30 + 5a <=16 ?

Apr 16, 2018

I really don't know how to explain it to you but I will try.

#### Explanation:

You add 30 on both sides to cancel the 30 and leave the 5a by itself. 30 cancels out since you added 30, and 16 plus 30 is 46. When 30 cancels out and 5a is by itself, you just divide by five both sides. 5a divided by 5 is a, and 46 divided by 5 is 9.2, and if you have to round it by the nearest tenth, then the answer is just 9.

Apr 16, 2018

$a \le 9 \frac{1}{5}$

#### Explanation:

$- 30 + 5 a \le 16 \rightarrow$ Add $30$ to each side

$5 a \le 46 \rightarrow$ Divide each side by $5$

$a \le 9 \frac{1}{5}$

Apr 17, 2018

$\text{ }$
Solution: color(blue)(a<= 46/5

Using Interval Notation : color(blue)((-oo, 46/5)

#### Explanation:

$\text{ }$
Given the Inequality expression: color(red)(-30+5a<=16

Rearrange the terms in $- 30 + 5 a \le 16$

$5 a - 30 \le 16$

Add $\textcolor{red}{30}$ to both sides of the inequality

$5 a - 30 + \textcolor{red}{30} \le 16 + \textcolor{red}{30}$

$5 a - \cancel{30} + \textcolor{red}{\cancel{30}} \le 16 + \textcolor{red}{30}$

$5 a \le 46$

Divide both sides of the inequality by $\textcolor{red}{5}$

$\frac{5 a}{\textcolor{red}{5}} \le \frac{46}{\textcolor{red}{5}}$

$\frac{\cancel{5} a}{\textcolor{red}{\cancel{5}}} \le \frac{46}{\textcolor{red}{5}}$

$a \le \frac{46}{5}$

Hence, the required solution is given by color(blue)(a<= 46/5

Using Interval Notation : color(blue)((-oo, 46/5)

You can verify the solution with a graph: