Writing, Solving and Graphing Inequalities

Writing, Solving and Graphing Inequalities

Follow along using the guided worksheet

Inequalities

We have 4 different comparison signs:

1. Greater than

2. Less than

3. Greater than or equal to

4. Less than or equal to

Multiple Choice

 What is this inequality?

 $>$ 

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality?

 $\le$ 

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality?

 $<$ 

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality?

 $\ge$ 

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Now we need to interpret what these inequalities mean

For example,  $y\ \le\ 3$ means  $y$  could be 3, 2, 1, 0, -1, -2, .... and on and on!

Let's see if YOU can interpret these inequalities

Multiple Select

Choose all of the numbers that satisfy the inequality below:

 $h\ >\ 12$  

• 12

• 16

• 10

• 23

• 14

Multiple Select

Choose all of the numbers that satisfy the inequality below:

 $t\ \le-4$  

• -8

• -4

• 4

• 2

• -100

Writing Inequalities

When writing inequalities:

1. Choose a variable

2. Determine what comparison sign you should use

3. Identify the number that should be used

Multiple Choice

Josh has to have at least $10 before going to the mall.

•  $j\ <\ 10$  

•  $m\ \ge\ 10$  
  

•  $x\ >\ 10$  
  

Multiple Choice

Beyonce has at most 24 Grammy awards.

•  $g\ \le\ 24$  

•  $B\ <\ 24$  
  

•  $a\ >\ 24$  
  

Multiple Choice

Peterson wants to try on more than 5 super bowl rings.

•  $P\ >\ 4$  

•  $r\ \ge\ 5$  
  

•  $s\ >\ 5$  
  

Solving Inequalities

We use the same steps as solving equations.

The inequality will stay the same with one exception:

When multiplying or dividing by a negative number, you have to FLIP the inequality.

What does "flipping" the inequality mean?

 $2-2x\ \ge\ 4$  

Step one: subtract 2 on both sides: 
 $-2x\ \ge\ 2$  

Step two: divide both sides by  $-2$  

 $\frac{-2x}{-2}\ \ge\ \frac{2}{-2}$             $\rightarrow$           FLIP           $\rightarrow$       $x\ \le\ -1$  

Are you ready to solve one and two step inequalities?

No? Let's do it anyways...

Fill in the Blanks

Solve. Write you answer as a solution set ( ex:  g > 3 ).
 $g-5>12$  

Fill in the Blanks

Solve. Write you answer as a solution set ( ex:  g > 3 ).
 $5f<-15$  

Fill in the Blanks

Solve. Write you answer as a solution set 

** To write greater/less than or equal to, type an equal sign after the inequality <= or >=   

 $\frac{x}{3}\ge6$  

Fill in the Blanks

Solve. Write you answer as a solution set 

** To write greater/less than or equal to, type an equal sign after the inequality <= or >=   

 $g+14\ \le\ -2$  

Fill in the Blanks

Solve. Write you answer as a solution set 

** To write greater/less than or equal to, type an equal sign after the inequality <= or >=   

 $3p\ +\ 10\ >\ 4$  

Fill in the Blanks

Solve. Write you answer as a solution set 

** To write greater/less than or equal to, type an equal sign after the inequality <= or >=   

 $-2y\ <\ 20$  

Fill in the Blanks

Solve. Write you answer as a solution set 

** To write greater/less than or equal to, type an equal sign after the inequality <= or >=   

 $\frac{a}{-5}\ \le\ -10$  

Poll

How are you doing so far?

• Inequalities are easy!

• Not bad so far

• I need some help still

• This doesn't make sense yet

Graphing Inequalities

When graphing inequalities, we use horizontal number lines.

(horizontal = sideways)

How to graph inequalities:

• #1:  Decide if there should be an open of closed circle on the number

•       Less than  $\leftrightarrow$  open circle

•       Greater than  $\leftrightarrow$  open circle

•       Less than or equal to  $\leftrightarrow$  closed circle

•       Greater than or equal to   $\leftrightarrow$  closed circle

Multiple Select

Select the key features when graphing the inequality below:

 $k\ \ge\ 6$  

• Open circle at 6

• Closed circle at 6

•  $\leftarrow$  
  Left arrow

•  $\rightarrow$  
  Right arrow

Multiple Select

Select the key features when graphing the inequality below:

 $m\ <\ -3$  

• Open circle at-3

• Closed circle at -3

•  $\leftarrow$  
  Left arrow

•  $\rightarrow$  
  Right arrow

Multiple Select

Select the key features when graphing the inequality below:

 $y\ \le\ 100$  

• Open circle at 100

• Closed circle at 100

•  $\leftarrow$  
  Left arrow

•  $\rightarrow$  
  Right arrow

Multiple Select

Select the key features when graphing the inequality below:

 $c\ >\ 0$  

• Open circle at 0

• Closed circle at 0

•  $\leftarrow$  
  Left arrow

•  $\rightarrow$  
  Right arrow

Good job!

What section did you do the best in?

What did you struggle with?

Poll

My BEST section with inequalities was:

(if there was more than one, select all that apply)

• Solving

• Writing

• Graphing

• I liked them all!

Poll

My WORST section with inequalities was:

(if there was more than one, select all that apply)

• Solving

• Writing

• Graphing

• I struggled on all :(