# How do you solve and graph 4>=2y-5>=-2?

##### 1 Answer

$\frac{9}{2} \ge y \ge \frac{3}{2}$

To graph this, place solid dots over $\frac{9}{2}$ and $\frac{3}{2}$ (to indicate that both points are part of the solution) and connect the two points with a line segment.

#### Explanation:

When approaching a problem like this, we're actually doing two inequalities at the same time. What we do to the middle we must do to both sides:

$4 \ge 2 y - 5 \ge - 2$

We can add 5 to all sides:

$4 \textcolor{red}{+ 5} \ge 2 y - 5 \textcolor{red}{+ 5} \ge - 2 \textcolor{red}{+ 5}$

$9 \ge 2 y \ge 3$

And now divide all sides by 2:

$\frac{9}{\textcolor{red}{2}} \ge \frac{2 y}{\textcolor{red}{2}} \ge \frac{3}{\textcolor{red}{2}}$

$\frac{9}{2} \ge y \ge \frac{3}{2}$

To graph this, place solid dots over $\frac{9}{2}$ and $\frac{3}{2}$ (to indicate that both points are part of the solution) and connect the two points with a line segment.