Compound Inequalities

Compound Inequalities

by Deb Scott

Objective: Solve Compound Inequalities

Compound Inequalities

Two Inequalities (or more) joined together with "and" or "or"

Type 1:"Or"

"or" inequalities have a tendency to graph apart

Solving "Or" Compound Inequalities

Our first step is to solve the inequalities for the given variable

Graphing "Or" Compound Inequalities

Once you solve the inequalities, it is time to graph! Graph just as you would any other Inequality. Notice how the two inequalities go in opposite directions.

Multiple Choice

Solve the following Compound Inequality $$3x\ge9\ or\ 5+x<6$$

• $$x<1\ or\ x\le3$$

• 

  $$x<1\ or\ x\ge3$$

• $$x<1\ or\ x\ge-3$$

• $$x<1\ or\ x\le-3$$

Multiple Choice

Does the following graph match the compound inequality

$$x<1\ or\ x\ge3$$  

• True

• False

Multiple Choice

Solve the following Compound Inequality $$2x+9>17\ or\ 5x+10<10$$  

• $$x<0\ or\ x<4$$  

• $$x>0\ or\ x>4$$  

• $$x<0\ or\ x>4$$  

• $$x>0\ or\ x<4$$  

Multiple Choice

Solve the following Compound Inequality $$-3\left(2x+1\right)<-15\ or\ 1-x\ge5$$  

• $$x\ge2\ or\ x\le-4$$  

• $$x\le-4\ or\ x>2$$  

• $$x\ge-4\ or\ x<2$$  

• $$x<-4\ or\ x>2$$  

Type 2: "And"

"and" inequalities have a tendency to graph together

Rewriting "And" Inequalities

Because the solutions to an "and" inequality fall between two endpoints, they are frequently written in a more condensed form.

Solving "and" Compound Inequalities

You must split the compound inequality into two inequalities. You can use the box method to help you split the compound inequality in two. Notice in the picture how everything in the middle is included when splitting it in two.

Graphing "And" Compound Inequalities

Once you solve the inequalities, it is time to graph! Graph just as you would any other Inequality. Notice how the two inequalities go towards each other.

Multiple Choice

Solve the following "and" Compound Inequality

$$-27<7x-13<8$$  

• $$x>-2\ and\ x<3$$  

• $$x<-2\ and\ x<3$$  

• $$x>-2\ and\ x>3$$  

• $$x>2\ and\ x<3$$  

Multiple Choice

Which compound inequality  matches the following "And" Compound Inequality

$$x>-2\ and\ x<3$$  

• $$-2<x<3$$  

• $$-2>x<3$$  

Multiple Choice

Which graph matches the following "And" Compound Inequality

$$x>-2\ and\ x<3$$  

Multiple Select

Solve the following the Compound Inequality $$-2<2\left(x-6\right)\le4$$  

• $$5<x\le8$$  

• $$5>x\ge8$$  

• $$x<5\ and\ x\ge8$$  

• $$x>5\ and\ x\le8$$  

Poll

How do you feel about solving Compound Inequalities?

• Great

• Good

• Okay

• More Help