x < 7 x > 3 x 9 2x - 6 = x = 4 3x = x = x = -2 x = 7 5x + 8 > 23 2x 4 14 x + 3 < NOTES Solving Multi Step Inequalities

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1 BELLWORK: Solve each equation. A) x 16 = 12 B) 3x + 5 = 1 C) 2(x 3) = x = x = x = -2 2x - 6 = x = x = 7 LESSON Solving Multi-Step Inequalities Works very similar to solving linear equations. EXCEPTION:If you multiply or divide both sides by a negative number, you must reverse the inequality. 2x + 6 > 8-2x > 2 x < -1 x + 3 < x < 7 NOTE: The answer may be ʺNo solutionʺ or ʺInfinitely many solutions.ʺ This process works very similar to solving equations as well. NO SOLUTION: If all the variables cancel out and you are left with a FALSE statement (ex: 7 < 5), then the answer is ʺNo solution.ʺ The graph would be empty. INFINITELY MANY SOLUTIONS: If all the variables cancel out and you are left with a TRUE statement (ex: 5 < 7), then the answer is ʺInfinitely many solutions.ʺ Shade the entire number line to represent this answer. 2x x x 9 5x + 8 > x > x > 3

2 6x x x 2 x x x 6 6x 10 > x > 12 x < x x 8 x > 9x > 9x > x x < x x x x -3

3 x x x x 5 5x 7 < 7x 6-7x -7x -2x - 7 < x < 1 x > x x 13-9x -9x -6x x -30 x 5 8x + 3 < 8x 5-8x -8x 3 < -5 FALSE. No solution. 3(5x 9) < 63 15x - 27 < x < x < 6 4(3x + 10) 8-12x x x -4

4 2(5 7x) 3x x 3x x -3x x x x 4 7x 25 > 3(2x 9) 7x - 25 > 6x x -6x x - 25 > x > -2 4(6x 2) < 8(3x + 2) 24x - 8 < 24x x -24x -8 < 16 TRUE. Infinitely many solutions. Tyler wants to get at least an 80% in Mr. Williamʹs class. His grade is based on the 5 tests that they will take this semester. His test scores so far are 73%, 92%, 67%, and 78%. What score must Tyler get on the last test in order to achieve his goal of having 80% overall in the class? x ( x ) (80) x x x 90 Tyler must get at least a 90% on the last test to have an 80% for the class overall. Diane wants to buy a new phone, which will cost $250. She has already saved up $82. She babysits for the Harrisons and earns $30 per night. How many nights must she babysit in order to save up enough money to buy her new phone? x x x 5.6 Diane should babysit 6 nights for the Harrisons so she has enough money to buy the phone. Kristy wants to bake cookies for her family reunion. She estimates that there will be about 70 people there. She wants to bake enough cookies for everyone to have at least two. She has already baked 1 batch of cookies, which made 24 cookies. How many more batches must she bake to make enough for everyone at the reunion to have two cookies? x 70(2) x x x 4.8 Kristy should bake 5 more batches of cookies in order to have enough so that everyone at the reunion can eat 2 cookies.

5 HOMEWORK: 2.4 Worksheet Solving Multi Step Inequalities