Warm Up Graph each set of numbers on a number line. -3, 7, -9 -2, -10, -8 3, -6, 10

Graphing Inequalities

Alex and Billy had a race! Alex is faster than Billy! FINISH Alex Billy

Do Alex and Billy have equal speeds? Let a = Alex’s speed and b = Billy’s speed Does a = b? No! a > b

We call things like a > b inequalities because they are not equal. Symbol Words Example > greater than 5 > 2 < less than 7 < 9

Inequalities are easy to remember Inequalities are easy to remember. The small end always points to the smaller number. BIG small BIG small

Example: Jacob plays under 15 soccer. How old is Jacob? Let j = Jacob’s age j < 15 The small end points to j because Jacob’s age is smaller than 15.

We can also have inequalities that include equals, like this: Symbol Words Example Use ≥ greater than or equal to x ≥ 1 ≤ less than or equal to y ≤ 3

Example: You must be 13 years or older to watch a movie. Let y be your age. y ≥ 13

How do we graph inequalities? Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. ○ for > and < ● for ≥ and ≤ Step 3: Draw an arrow in the direction of the inequality.

Example: x < 2 Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. Closed circle if the number is included, open circle if it is not. Step 3: Draw an arrow in the direction of the inequality.

Example: x ≥ -3 Step 1: Draw a number line. Step 2: Place a circle on the number in the inequality. Closed circle if the number is included, open circle if it is not. Step 3: Draw an arrow in the direction of the inequality.

You try! Graph the following inequalities: z < -2 4 > t a ≥ -5 2 ≤ c