# How do you solve and graph #-5 < (t + 15)/3 ≤ 9#?

##### 1 Answer

#### Explanation:

There are two inequalities here combined into one line. Separately, they look like this:

(a)

(b)

Generally speaking, to solve an inequality, like

It's important that the latter inequality is completely equivalent to the former, that is from

In this case we can apply a few *invariant* transformations to the original inequality to obtain this final result as follows.

Step 1. Both parts of an inequality can be multiplied by the same positive number. So, let's multiply each inequality by

(a)

(b)

Step 2. The same number can be added to both parts of an inequality. Let's add

(a)

(b)

Basically, we have completed our task. We know now that the condition

The latter form constitutes the solution.

Graphically, it's represented by an interval of real values of variable

In short, it can be written as

(notice parenthesis used for the left boundary and square bracket for the right, signifying not including and including the border into the interval).

We can recommend to study this material at Unizor by following the menu items *Algebra - Introduction to Inequalities*.