Question

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

Answer 1

`9/2>=y>=3/2`

To graph this, place solid dots over `9/2` and `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 >= 2y-5 >= -2`

We can add 5 to all sides:

`4color(red)(+5) >= 2y-5color(red)(+5) >= -2color(red)(+5)`

`9>=2y>=3`

And now divide all sides by 2:

`9/color(red)(2)>=(2y)/color(red)(2)>=3/color(red)(2)`

`9/2>=y>=3/2`

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