Objective The student will be able to: graph inequalities on a number line. solve inequalities using addition and subtraction. solve inequalities using multiplication and division Designed by Skip Tyler, Varina High School Modified by Lisa Hoffmann, Troy Buchanan High School

Warm Up Pg 332 # 1-9

Warm Up Answers Yes No 10 24 9

1) Graph the solution set of x < 3. When you have < or >, use an open dot!

2) Graph the solution set of y ≥ -5/4. • When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

3) Graph the solution set of p ≠ 2. When you have ≠, use an open dot and shade both ways!

4) Which inequality would have a closed dot on the number line? > < ≥ ≠ Answer Now

5) Which inequality does NOT use an open dot on the number line? ≤ < > ≠ Answer Now

6) Solve x + (-14) < 16 x - 14 < 16 + 14 + 14 x < 30 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16 Solve this problem like an equation Draw “the river” Eliminate double signs Add 14 to both sides Simplify Check your answer Graph the solution o 30 31 29

7) Solve y + 21 ≥ 7 y ≥ -14 30 + (-14) = 16 16 = 16 ● - 21 -21 -14 -13 - 21 -21 y ≥ -14 30 + (-14) = 16 16 = 16 Draw the “river” Subtract 21 from both sides Simplify Check your answer Graph the solution -14 -13 -15 ●

9) What is the graph of 7 ≤ m? ● ● o o 7 8 6 7 8 6 7 8 6 7 8 6 Answer Now

12) Joanna’s tests were 87, 93, 88 and 94 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? 96 97 98 100 Answer Now

1) Which graph represents the correct answer to > 1 -4 16 -20 Remember to use a test point on each side of –4. Whichever one works is the direction you shade! o -4 16 -20 ● -4 16 -20 ● -4 16 -20 Answer Now

Rules for Solving Inequalities You can add the same number (positive or negative) to each side of the inequality You can subtract the same number (positive or negative) from each side of the inequality You can multiply OR divide both sides of an inequality by a positive number WHEN YOU MULTIPLY OR DIVIDE EACH SIDE OF THE INEQUALITY BY A NEGATIVE NUMBER YOU MUST CHANGE THE DIRECTION OF THE INEQUALITY SYMBOL!

1) Solve > 13 -4 · k < 13 · -4 -4 k < -52 o -52 -51 -53 Draw “the river” Clear the fraction - Multiply both sides by -4 NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! Simplify Check your answer Graph the solution k < -52 o -52 -51 -53

2) When solving > -10 will the inequality switch? Yes! No! I still don’t know! Answer Now

2) Solve < -10 x < -30 3 • x < -10 • 3 3 o -30 -29 -31 Draw “the river” Clear the fraction - Multiply both sides by 3. Do you switch the inequality? No - Both sides are being multiplied by a positive number Simplify Check your answer Graph the solution 3 • x < -10 • 3 3 x < -30 o -30 -29 -31

3) Solve x > -24 -4 • -a > 6 • -4 -4 o -24 -23 -25 Draw “the river” Clear the fraction - Multiply both sides by -4. Do you switch the inequality? Yes - Both sides are being multiplied by a negative number Simplify Check your answer Graph the solution -4 • -a > 6 • -4 -4 x > -24 o -24 -23 -25

4) Solve -8p ≥ -96 p ≥ 12 p ≥ -12 p ≤ 12 p ≤ -12 Answer Now