Solving Linear Inequalities

Introduction to Inequalities

Identifying and Graphing Inequalities

​Dr. Tom Giles

Introduction to Inequalities

INEQUALITY

Greater Than ( > )

• is greater than

• is more than

• mas grande que

Less than ( < )

• is less than

• is fewer than

• menos que

Greater Than or Equal To

• is greater than or equal to

• is at least

• is no less than

Less Than Or Equal To

• is less than or equal to

• is at most

• is no more than

Multiple Choice

What symbol could go in the box to make a true statement?
71  ___  2

• >

• <

• ≥

• ≤

Multiple Choice

Less Than

• <

• >

• ≤

• ≥

Multiple Choice

Which inequality symbol is being shown in the picture?

• greater than

• less than

• less than or equal to

• greater than or equal to

Multiple Choice

• less than

• greater than

• less than or equal to

• greater than or equal to

Solution (answer) of an Inequality

• a value that makes the inequality true

• an inequality can have MORE THAN ONE solution

Multiple Choice

Is 4 a possible solution for p ≥ -8 ?

• Yes

• No

Multiple Choice

Is 9 a possible solution for k<7 ?

• Yes

• No

Multiple Select

Choose ALL the values that are a solution to x $$\le$$  4 

• -2

• 0

• 4

• 6

• 14

Graph of an inequality

Multiple Select

Which inequality symbol(s) has a graph with an OPEN circle?

• <

• ≤

• >

• $$\ge$$  

Multiple Choice

Would you use a closed or open circle to graph x < 3?

• Closed

• Open

Multiple Choice

Match the graph with its inequality.

• c > 9

• c < 9

• c ≥ 9

• c ≤ 9

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

Solve the inequality: 

2x+5 $$\ge$$  15

• x $$\ge$$  2.6

• x $$\ge$$  10

• x $$\ge$$  20

• x $$\ge$$ 5

Multiple Choice

Solve the inequality

• $$x\le3$$

• $$x\ge3$$

• $$x\ge2.5$$

• $$x\le2.5$$

Multiple Choice

Solve the inequality

• $$-1>n$$

• $$-1<n$$

• $$.429>n$$

• $$-\frac{1}{5}>n$$

• $$4<n$$

Multiple Choice

Solve the inequality

• $$r\ge6$$

• $$r\le6$$

• $$r\le11.25$$

• $$r\ge11.25$$

• $$r\ge13.625$$

Solve Absolute Value Inequalities

Essential Question: What are the differences between solving absolute value equations vs. inequalities?

I can solve an absolute value inequality algebraically

Greater than (>)

Greater than equal to (>)

Remember GREAT "OR"

Multiple Choice

Solve the absolute value inequality.

$$\left|2x-1\right|<3$$  

• $$x<-1\ or\ x>2$$  

• $$1<x<2$$  

• $$-1<x<2$$   

• $$-1>x>2$$  

Open Ended

What would be the first step to isolate the absolute value?

$$9\left|x+4\right|+10\le55$$  

Multiple Choice

What would be the next step to isolate the absolute value? $$9\left|x+4\right|\le45$$  

• Divide by 9

• Add 9

• Subtract 4

• Multiply by 9

Multiple Select

Which two inequalities below would be the next step? Click two below

$$\left|x+4\right|\le5$$  

• $$x+4\le-5$$

• $$x+4\ge5$$

• $$x+4\le5$$

• $$x+4\ge-5$$

Multiple Choice

Solve the absolute value inequality.

$$6\left|x+3\right|-10\ge-4$$  

• $$x\le-4\ or\ x\ge-2$$  

• $$-4<x<-2$$  

• $$-2<x<4$$   

• $$x\le-4\ or\ x\ge2$$  

Open Ended

Write in your own words the steps to solve absolute value inequalities.

Multiple Choice

• v>5 or v<-5

• v≥5 or v≤-5

• v>-5 or v<5

• all real numbers

Multiple Choice

• no solution

• a> -1/6 or a< -5/6

• a>1/2 or a< -3/2

• all real numbers

Multiple Choice

• no solution

• -6 ≤ r ≥ 8

• 6 > r > -8

• -6 < r < 8

Multiple Choice

• n > 1 or n < -7

• n > -1 or n < -7

• -7 < n < -1

• no solution

Multiple Select

Which two inequalities below would be the next step in solving 

$$\left|x+6\right|<2$$  

• $$x+6<-2$$  

• $$x+6>-2$$  

• $$x+6<2$$  

• $$x+6>2$$  

• $$x+6=2$$  

Less than ( <)

Less than equal to( <)

Remember LESS "AND"