Compound Inequalities

Multiple Choice

WARM UP: What inequality does the number line graph represent

• $$x<-4$$

• $$x>-4$$

• $$x\le-4$$

• $$x\ge-4$$

Compound Inequalities

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

Type 1:"Or"

"or" inequalities have a tendency to graph apart

Type 2: "And"

"and" inequalities have a tendency to graph together

Graphing Compound Inequalities

Using the word "OR"

Multiple Select

Which inequalities represent the graph?

_______ or _______

• $$x\ge-10$$

• $$x\le-10$$

• $$x>20$$

• $$x<20$$

• $$-10\le x<20$$

Multiple Choice

Which graph represents  $$x\le-4$$  or  $$x>0$$  ?

Graphing Compound Inequalities

Using the word 'AND'

​A compound inequality is an inequality that combines two simple inequalities.

EXAMPLE

Graph x ≥ 4 and x < 7

Draw

Graph the following inequality:

$$x\ge4\ and\ x<7$$  

Draw

Graph the following inequality:

$$x>-3\ and\ x<4$$  

Another way to write the Inequalities

When they use the word 'AND'

​

low number < x < high number

​

Example: x < 10 and x ≥ -2

​

-2 ≤ x < 10

The numbers become the endpoints, just use the proper inequality symbol.

Draw

Graph the following inequality:

$$-1\le x\le9$$  

Multiple Choice

Which graph represents the compound inequality  $$-5<x<15$$  ?

Multiple Choice

Which graph matches the following "And" Compound Inequality

$$x>-2\ and\ x<3$$  

Multiple Choice

Which value of x makes the following Compound Inequality true $$-3<2x+3\le15$$  

• $$x=8$$  

• $$x=-3$$  

• $$x=5$$  

• $$x=7$$  

Multiple Select

Which value of x makes the following Compound Inequality true $$-2<2\left(x-6\right)\le4$$  

• $$x=5$$  

• $$x=-2$$  

• $$x=0$$  

• $$x=7$$  

Multiple Choice

Which value of x makes the following Compound Inequality true

$$-27<7x-13<8$$  

• $$x=2$$  

• $$x=0$$  

• $$x=3$$  

• $$x=-2$$  

Multiple Choice

Which value of x makes the following Compound Inequality true $$2x+9>17\ or\ 5x+10<10$$  

•   $$x=2$$  

•   $$x=5$$  

Multiple Choice

Which value of x makes the following Compound Inequality true

$$3x\ge9\ or\ 5+x<6$$

• $$x=-5$$  

• 

  $$x=2$$