Solving & Graphing Inequalities PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line. LT 3: Solve two inequalities. Materials Needed Individual Interactive Notebooks Pencil Answer Sheet

You learned that an INEQUALITY compares using symbols: Write this expression in words > (6)(7) (9)(5) 66 ÷ 2 (8)(4) – 3 – 7 – 3 + 7 Comparison Practice

Algebraic Inequalities You learned that ALBEBRAIC INEQUALITIES contain Variables: b > ½ x ≥ 7 Write Three of Your Own Algebraic Inequalities k ≤ 100 5.9 < m f ≤ 13

A SOLUTION makes the inequality TRUE. (5)(3) 14 ? The Inequality 15 14 < The solution Solve Problem Written with Solution Circled 1) 34 17 ● 2 2) 54 ÷ 9 5 3) (16)(3) 23 + 18

A SOLUTIONS SET is a RANGE of possible answers “It anywhere from ____ to ____. Fill in the empty boxes 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 ≤ -3 3) y > 11

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 > 10 w < -7

One-Step Inequalities

Solving for Inequalities is EXACTLY like EQUATIONS. YOU KNOW THIS SIDE! Solution Set x + 7 = 10 x + 7 ≤ 10 - 7 = - 7 - 7 ≤ - 7 x = 3 x ≤ 3 Subtract 7 From both Sides. Bring down what’s left. Equals line closed 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 3 or lower.

a + 6 ≥ 8 24 ≤ 6w ─ 6 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 ─ 2 < 3 > -1 4 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. Insert an arrow going in the correct direction below.

Practice x + 6 > 15 2. y + 8 < 8 3. 5z ≤ 35 4. a – 7 ≥ 13 b 6 Inequality Solution Set x + 6 > 15 2. y + 8 < 8 3. 5z ≤ 35 4. a – 7 ≥ 13 b 6 > 3

Two-Step Inequalities

Solving for 2 step Inequalities is EXACTLY like EQUATIONS. YOU KNOW THIS SIDE! Solution Set 5x + 8 = 18 5x + 8 ≤ 18 - 8 = - 8 - 8 ≤ - 8 5x = 10 5x ≤ 10 5 5 x = 2 x ≤ 2 Subtract 8 From both Sides. Divide by 5 on both Sides. Q: Why don’t we graph the equation? A: We know the answer, it’s 2. Q: Why do we graph the inequality? A: To show all possible answers. We’re not sure exactly, but we know it’s 2 or lower.

5a ─ 5 > 10 18 < 6w + 6 5a < 6w < w + 5 > a > Example 1 Example 2 5a ─ 5 > 10 18 < 6w + 6 + 5 5a > < 6w a > < w Insert an arrow going in the correct direction below. Insert the appropriate open or closed point below.

w 2k + 12 ≤ 12 4 + 5 ≥ 8 ≤ k w ≥ Example 3 Example 4 Write the SOLUTION SET FOR examples 3 and 4 below.

Practice 3x + 14 > 38 2. 5y – 5 < 55 3. 3z – 15 ≤ 15 Inequality Solution Set 3x + 14 > 38 2. 5y – 5 < 55 3. 3z – 15 ≤ 15 4. 3a – 3 ≥ 0 b 2 + 6 > 6