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

1 Answer

Answer:

#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.