Compound Inequalities (A1 1-6)

Compound Inequalities (A1 1-6)

ESSENTIAL 

​QUESTION

​WHAT ARE COMPOUND INEQUALITIES AND HOW ARE THEIR SOLUTIONS REPRESENTED?

​COMPOUND INEQUALITY

Two inequalities (or more) joined together with "and" or "or".​

TYPE 1: "OR" :

"or" inequalities tend to graph apart

​

​<----- or ----->

example 1:

FIrst, solve the inequalities for the given variable.

example 1:

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.

example 2:

Multiple Choice

Solve the following Compound Inequality:  $$2x+9\ge17\ \ \ or\ \ \ 5x+10<10$$  

• $$x>4\ \ or\ \ x\ge0$$  

• $$x\ge4\ \ or\ \ x>0$$  

• $$x\le4\ \ or\ \ x\ge0$$  

• $$x\ge4\ \ or\ \ x<0$$  

Multiple Choice

Does the following graph match the compound inequality: $$x\ge4\ \ or\ \ x<0$$  

• TRUE 

• FALSE 

Multiple Choice

Solve the following Compound Inequality: $$7x-14\ge0\ \ \ or\ \ \ 4x+5\le-3$$  

• $$x\le-2\ \ or\ \ x>2$$  

• $$x\le-2\ \ or\ \ x\ge2$$  

• $$x\le2\ \ or\ \ x>-2$$  

• $$x<-2\ \ or\ \ x>2$$  

Multiple Choice

Solve the following Compound Inequality: $$−3(2x+1)<−15\ \ \ or\ \ \ 1−x\ge5$$  

• $$x\ge2\ \ or\ \ x\le−4$$  

• $$x\ge−4\ \ or\ \ x<2$$  

• $$x\le−4\ \ or\ \ x>2$$  

• $$x<−4\ \ or\ \ x>2$$  

TYPE 2: "AND" :

"and" inequalities have a tendency to graph together

TYPE 2: "AND" :

Because "and" solutions fall between two endpoints, they can be written in a condensed form:

Solving "and":

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.

Solving "and":

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.

ex. 2:

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 Choice

Solve the following Compound Inequality: $$−3<2x+3\le15$$  

• $$x>−3\ \ and\ \ x\ge6$$  

• $$x<−3\ \ and\ \ x<6$$  

• $$−3>x\le6$$  

• $$x>−3\ \ and\ \ x\le6$$  

Multiple Select

Solve the following the Compound Inequality:   $$−2<2(x−6)\le4$$  

• $$5<x\le8$$  

• $$x<5\ \ and\ \ x\ge8$$  

• $$5>x\ge8$$  

• $$x>5\ \ and\ \ x\le8$$  

Poll

How do you feel about solving Compound Inequalities?

• Great!

• Good

• Okay

• More Help