Solving Inequalities

What is an inequality? Better known as “pac-man’s” Compares the left side to the right side. Four different inequality symbols:

< less than

> greater than

≤ less than or equal to

≥ Greater than or equal to

Pac man eats the larger side so you can easily remember which symbol is which.

How do I solve equations with them? Solve them just like regular equations.

1. Distribute2. Move plain numbers to the right3. Move variables to the left4. Solve.

KEEP YOUR INEQUALITY CORRECT!! Adding or subtracting will not change your

symbol. If you multiply or divide by a negative number

you MUST flip your inequality.

Example 1Solve

Answer: m ≥ 3

363 m

Example 2Solve 23

52 d

Example 3Solve 29217 qq

Example 4Solve rr 1024159

Example 5Solve w

w2

4

53

Example 6Solve 7 + 3r ≤ 2(r+3) – 2(-1 – r)

Example 7Solve 3y + 4 > 2(y+3) + y

What do their graphs look like? Back to the number line…

Create your number line with at least three numbers on it

Decide if it should be an open or closed dot > or < open dot ≥ or ≤ closed dot

Figure out which way your arrow should go. Pac man eats the variable, shade right. Pac man eats the number, shade left.

Graph Example 1 solution