Lesson 1: Graphing and Writing Inequalities

Inequalities

Remember, there are two sides to an inequality! The greater than side and the less than side.

Multiple Choice

How many solutions are there to the equation  $2x+1=7$  ?

• one

• two

• three

• infinite

Poll

How many solutions do you think the inequality  $3+x>5$  has?

• one

• two

• three

• infinite

Open Ended

Write one solution to the inequality

 $y\le9.2$  

Open Ended

Write one solution to the inequality

 $2x-1>7$  

Open Ended

What do you think makes a value a "solution" to an inequality?

Solutions to Inequlities

• Any value that makes the inequality true is a solution

• Unlike equations, inequalities have a range of solutions

Graphing Solutions to Inequalities

• An inequality like

   $3+x<9$  has too many solutions to list
  

• We can use a graph on a number line to show all solutions

• The solutions continue past the arrow to the left!

Open vs Closed

An open circle indicates < or > , meaning that we do not include the starting number.

A closed circle indicates

 $\le$  or  $\ge$  , meaning that we do include the starting number.

Multiple Choice

A(n) _________ circle indicates that the starting number is also a solution to the inequality.

• open

• closed

Multiple Select

Select all the inequalities that would be graphed with a closed circle.

• $2x+3\ge-4$

• $5<8-x$

• $2y\le6$

• $9m-19>14+m$

• $y<3$

Write an inequality to match the number line graph. Can you think of more than one inequalities that match?