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Name: Date: Period: Topic: Solving Inequalities Essential Question: What is the correlation between solving equations and solving inequalities? Warm-up: Name the following inequality signs: Inequality Symbols Less than Less than or equal to Greater than Not equal to Greater than or equal to Vocabulary: An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: Solving the Inequality w+5<8 Note: We will use the same steps that we did with equations, if a number is added to the variable, we subtract the same number to both sides. Answer w+5<8 w + 5 -5 < 8 -5 w+0<3 w<3 All numbers less than 3 are solutions to this problem! Now you try it! 7>x–5 8 + r ≥ -2 x - 2 > -2 4+y≤1 x+2≤3 Answers to Practice Problems: 8 + r ≥ -2 8 -8 + r ≥ -2 -8 r + 0 ≥ -10 w ≥ -10 All numbers from -10 and up (including -10) make this problem true! x - 2 > -2 4+y≤1 x - 2 + 2 > -2 + 2 4 - 4 + y ≤ 1 - 4 x+0>0 x>0 All numbers greater than 0 make this problem true! y + 0 ≤ -3 y ≤ -3 All numbers from -3 down (including -3) make this problem true! Answers to Practice Problems: x+2≤3 x-5>7 x+2-2≤7-2 x–5+5>7+5 x+0≤5 x + 0 > 12 x≤5 x > 12 0 12 0 5 What do these means? x<5 x>4 x≤3 x≥2 How to graph the solutions > Graph any number greater than. . . x>4 open circle, line to the right < Graph any number less than. . . open circle, line to the left x<5 Graph any number greater than or equal to. . . closed circle, line to the right x≥2 Graph any number less than or equal to. . . closed circle, line to the left x≤3 Solving the Inequality <-2 15b < 60 Answers x>4 x<-8 <-2 15b < 60 15b < 60 15 15 b<4 That was easy!!! But wait there is one special case: ● Sometimes you may have to reverse the direction of the inequality sign!! ● That only happens when you multiply or divide both sides of the inequality by a negative number. Solving the Inequality - 4r > 16 Answers ( - 4r > 16 ( - 4r > 16 -4 -4 ( ( r<-4 m < - 10 Solving multi-step inequalities is like solving multi-step equations. If you can solve 2 x 3 11 you can solve 2 x 3 11 2 x 3 11 Remember: 2 x 3 11 Which graph shows the solution to 2x - 10 ≥ 4? Now you try it! Page 181 (1 – 4, 8, 16, 20) 1) 2) 3) 4) 5) 3(x + 4) - 5(x - 1) < 5 -2x + 6 ≥ 3x – 4 3 (t + 1) – 4t ≥ - 5 5m - 8 > 12 -5x – 9 < 26 Anytime you multiply or divide both sides of an inequality by a negative number, you need to reverse the sign. Wrap-Up: Brief Review of Inequalities • Add/subtract the same number on each side of an inequality • Multiply/divide by the same positive number on each side of an inequality • If you multiply or divide by a negative number, you MUST flip the inequality sign! Home-Learning: Page 175 (34), Page 176 (70), Page 181 (12, 21, 24), Page 189 (2, 4), Page 190 (20), Page 192 (59, 60)