Notes on Compound Inequalities

Compound Inequalities

Solving and Graphing

What are Compound Inequalities?

WHat Do They look Like?

Pay attention to which one is the closed circle and which is the
open circle. If we interpret this graph, it means the solution(s)
to our inequality are less than or equal to -2 OR greater than 3.

How do I solve an “or” compound inequality?

Solve each inequality like you would a regular
inequality. However, when you graph on a number
line, you will have two graphed lines instead of
one.

We divided by a negative, so remember to flip the sign.
Because we flipped the sign, now flip around the
inequalities to read from left to right on a number line.

You Try!

Complete #3 on your own. Check your answers for the compound
inequality on the next slide

​How did you do? Try #4 and #5. Answers are on the next slide for you to check.

Multiple Choice

What inequality is graphed? 

• x > 2 and x ≤ -3

• x > 2 and x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

Multiple Choice

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5

Multiple Choice

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5

• x < -5 and x > 5

• x < -5 or x > 5 

• x > -5 and x < 5 

The other Type of Inequality…

Notice that the smaller value comes first (-6) and then the
larger value (1).

This is read as “x is
greater than or equal
to -6 AND less than or
equal to 1”

When reading these types
of compound inequalities,
start at the middle, then
the left, then the right.

WHat Do They look Like?

If you draw two lines under each inequality symbol, use this
as your balancing of each side. What you do to one of the
sides, you must do to ALL three sides.

How do I solve An “AND” compound inequality?

In order to get “x” by itself (isolate), I needed to

subtract 4. Notice how I subtracted 4 from BOTH sides of the

inequality.

You Try!

Complete #7 on your page

How did you do?

Two -Step Inequality

Try the remaining Problems.

Multiple Choice

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

Multiple Choice

2<x+2<5

• 0<x<3

• 4<x<7

• 4<x<3

• 0<x<7

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What inequality is graphed?

• x > 2 and x < 4

• x ≥ 2 and x ≤ 4

• x > 2 or x < 4

• x ≥ 2 or x ≤ 4

Multiple Choice

Give the solution set for: -13<2x+5<15

• -9>x>5

• -9<x<5

• -4<x<5

• -4>x>5