Solving & Graphing Inequalities PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line. LT 2: Solve one-step inequalities. Materials Needed Individual Interactive Notebooks Pencil Answer Sheet

You learned that an INEQUALITY compares using symbols: > 1 Examples from Before > 2 > > Write the expression from example 1 in words. Write the expression from example 2 in words.

Comparison Practice 19 7 9 + 8 15 (9)(4) (12) (3) 16 ÷ 2 36 ÷ 4 19 7 9 + 8 15 (9)(4) (12) (3) 16 ÷ 2 36 ÷ 4 17 – 3 21 – 9 Comparison Practice

You learned that ALBEBRAIC INEQUALITIES contain Variables: x ≥ 7 k ≤ 100 5.9 < m Write Your Own Algebraic Inequality f ≤ 13

Now Write 3 more of your own Algebraic Inequalities

This makes the inequality You learned that a SOLUTION is the answer and makes the inequality TRUE. Example 1 21 - 6 14 ? 15 14 < The solution is 15, This makes the inequality TRUE.

Find the Solution of each Inequality Circle the Solution you found. Problem Written with Solution Circled 1) 59 10 + 41 2) 35 ÷ 7 7 3) (15)(2) 18 + 13

You learned that a SOLUTIONS SET is a RANGE of possible answers It’s like saying: “It’s might be 3, or any number lower than 3.

Use the completed squares to help you fill in the blank ones. Inequality In Words What are 3 possible solutions? Why? 1) x < 5 ‘x’ is less than 5 32, -7, 3 they are all less than 5 2) a ≥ 0 3) y ≤ -4

How to write answers for a SOLUTION SET? Arrows & Points How to write answers for a SOLUTION SET? For ‘less than’, the arrow points down When there is not an equals line, the point is open. f < 2 For ‘more than’, the arrow points up When there is an equals line, the point is closed. f ≥ 2

Graph the solution set for each inequality. Practice Which direction does the arrow go? 2) Is the point open or closed? Remember! Graph the solution set for each inequality. Inequality Solution Set x ≤ 1 h > -4 w < 4

Now that you have reviewed how to graph INEQUALITIES, you will learn to SOLVE them.

Solving for Inequalities is EXACTLY like EQUATIONS. YOU KNOW THIS SIDE! Solution Set x + 6 = 10 x + 6 < 10 - 6 = - 6 - 6 < - 6 x = 4 x < 4 Subtract 6 From both Sides. Bring down what’s left. No equals line open point Q: Why don’t we graph the equation? A: We know the answer, it’s 4. Q: Why do we graph the inequality? A: To show all possible answers. We’re not sure exactly, but we know it’s lower than 4.

Compare Equalities and Inequalities using the Venn Diagram. Equations How are they the Same?

a + 3 ≤ 5 18 ≥ 6w ─ 3 a ≤ ≥ w Example 1 Example 2 1. To solve, fill in the boxes above. 2. Insert an arrow going in the correct direction below. 1. To solve, fill in the boxes above. 2. Insert the appropriate open or closed point below.

w k ─ 0 < 0 > 4 3 k < ) ( ) ( > Example 3 Example 4 1. To solve, fill in the boxes above. 2. Write the SOLUTION SET FOR example 4 below. 1. To solve, fill in the boxes above. 2. Write the SOLUTION SET FOR example 3 below.

Practice x + 4 > 10 2. y – 5 < 5 3. 3z ≤ 15 4. a – 3 ≥ 6 b 2 Inequality Solution Set x + 4 > 10 2. y – 5 < 5 3. 3z ≤ 15 4. a – 3 ≥ 6 b 2 > 4