4.1 Inequalities

4.1 Review - Inequalities

An inequality is a mathematical sentence that compares expressions.  

•  $<$  is less than, is few than.

•  $>$  is greater than, is more than.

•  $\le$  is less than or equal to, is at most, is no more than.

•  $\ge$  is greater than or equal to, is no more than.

Multiple Choice

Choose the inequality that represents the statement

A number x is less than -10.

• $x<-10$

• $x>-10$

• x $x\le-10$

• $x\ge-10$

Multiple Choice

Choose the inequality that represents the statement

A number x is greater than 20.

•  $x<20$ 

•  $x>20$ 

•  $x\le20$ 

•  $x\ge20$ 

Multiple Choice

Choose the inequality that represents the statement

A number x is at most -15.

•  $x<-15$ 

•  $x>-15$ 

•  $x\le-15$ 

•  $x\ge-15$ 

Multiple Choice

Choose the inequality that represents the statement

A number x is at least 6.

•  $x<6$ 

•  $x>6$ 

•  $x\le6$ 

•  $x\ge6$ 

Multiple Choice

Choose the inequality that represents the statement

A number x is no more than -25.

•  $x<-25$ 

•  $x>25$ 

•  $x\le-25$ 

•  $x\ge25$ 

Multiple Choice

Choose the inequality that represents the statement

A number x is no less than 40.

•  $x<40$ 

•  $x>40$ 

•  $x\le40$ 

•  $x\ge40$ 

The graph of an inequality shows all of the solutions that makes the inequality true on a numberline.

• Use an open cirlce for  $<\ or\ >$  .

• Use a closed circle for  $\le or\ \ge$  .

• Greater values extend right on the numberline.

• Lesser values extend left on the numberline.

Multiple Choice

Describe the graph of the inequality

 $x>5$  

• Open circle at 5 with arrow extending right.

• Closed circle at 5 with arrow extenteding left.

• Closed circle at 5 with arrow extending right.

• Closed circle at 5 with arrow extending left.

Multiple Choice

Describe the graph of the inequality

 $p\le-15$  

• Open circle at -15 with arrow extending right.

• Closed circle at -15 with arrow extenteding left.

• Closed circle at -15 with arrow extending right.

• Closed at -15 circle with arrow extending left.

Multiple Choice

Choose the graph that represents the inequality

• A

• B

• C

• D

Multiple Choice

Choose the graph that represents the inequality

• A

• B

• C

• D

Multiple Choice

Choose the graph that represents the inequality

• A

• B

• C

• D

Multiple Choice

Choose the graph that represents the inequality

• A

• B

• C

• D

Checking Solutions for an inequality

• Substitute the given value for the variable.

• Evaluate the expression to see if the statement is true.

• Be careful comparing negative numbers.

Multiple Choice

Tell whether the given value is a solution of the inequality

 $n+8\le13,\ n=4$  

• YES

• NO

Multiple Choice

Tell whether the given value is a solution of the inequality

 $x-8\ge15;\ x=12$  

• YES

• NO

Multiple Choice

Tell whether the given value is a solution of the inequality

 $5y\le-9;\ y=-2$  

• YES

• NO

Multiple Choice

Tell whether the given value is a solution of the inequality

 $\frac{x}{4}\ge3;\ x=12$  

• YES

• NO