Intro to Inequalities

Intro to Inequalities

What is an inequality? Is this number a solution? How do I graph the solution set?

What is an inequality?

• a comparison between two numbers or expressions

• infinite possibilities for solutions

Multiple Choice

How many solutions do most inequalities have?

• 0

• 1

• 100

• infinite

Inequality Symbols

•  $<\ -\ less\ than$  
  

•  $\le-\ less\ than\ or\ equal\ to$  

•  $>\ -\ greater\ than$  

•  $\ge\ -\ greater\ than\ or\ equal\ to$  

Multiple Choice

What does the line under an inequality symbol mean?

• equal to

• not equal to

• it looks cool

How do I check if a number is a solution to an inequality?

How do I check if a number is a solution to an inequality?

Substitute the value into the inequality and simplify. If the result is a true inequality, it is a solution. If the result is not true, it is not a solution.

 $-2x+3>5$  

• Is  $x=7$  a solution?

• Substitute 7 into the inequality for x.  $-2\left(7\right)+3>5$  

• Simplify.  $-11>5$  

• Does this inequality make sense? No, so  $x=7$  is not a solution.

 $-2x+3>5$  

• Is  $x=-1$  a solution?

• Substitute -1 into the inequality for x.  $-2\left(-1\right)+3>5$  

• Simplify.  $5>5$  

Multiple Choice

Is $x=-1$  a solution?

• Yes =)

• No =(

Multiple Choice

Is $x=-5$  a solution to the inequality  $-2x+3>5$  ?

• Yes =)

• No =(

How can I find all the solutions to an inequality?

Inequalities have infinite solutions so we graph them to show all of the solutions at once.

Boundary Point

the end of the solution set for an inequality

Multiple Select

Which of these numbers are solutions to this inequality?

• 2

• 3

• 4

• 5

• 6

How do we graph the solutions to an inequality?

• Make a numberline with three tick marks. The boundary point goes in the middle. The numbers higher and lower than it go on either side.

• Graph a large point at the boundary point. This point should be open (donut) if it is not a solution and filled in if it is a solution.

• Check if the numbers to the left and right of the boundary point are solutions. Draw an arrow through the number that it a solution.

Multiple Choice

Which is the correct graph of $x<-3$  ?

Multiple Choice

Which is the correct graph of $x\ge-9$  ?

Open Ended

What new thing did you learn today about inequalities?