1. PRE-ALGEBRA

2. Lesson 7-5 Warm-Up

3. PRE-ALGEBRA “Solving Two-Step Inequalities” (7-5) (3-1) How do you solve a multi-step inequality? Tip: Solve a multi-step inequality exactly like an equality (equaltion with an equal sign). Isolate the variable (get the letter by itself) by: 1. “Undo”ing addition and subtraction from the variable side 2. “Undo”ing multiplication and division from the variable side Note: If the variables is on both sides, “undo” it from one side so that there is only one variable side before doing anything else

4. PRE-ALGEBRA Solve and graph 7g + 11 > 67. 7g + 11 > 67 7g + 11 – 11 > 67 – 11Subtract 11 from each side. 7g > 56Simplify. g > 8Simplify. Solving Two-Step Inequalities LESSON 7-5 Additional Examples Divide each side by 7. > 7g77g7 56 7

5. PRE-ALGEBRA Example: Solve 2y – 3  -5. 2y - 3 + 3  -5 + 3Add 3 to each side. 2y + 0  -2 Simplify. y  -1Simplify. Check: 2y - 3  -5 2y - 3  -5Check the direction of the inequality. 2(-2) - 3  -5Substitute a solution less than – 1 for b like -2. 2(-1) - 3 -5Substitute -1 for y. -5 = -5 -7  -5 The direction of the sign is correct.  Divide each side by 2. 2y 2 -2 2 “Solving Two-Step Inequalities” (7-5) (3-1)

6. PRE-ALGEBRA Example: Solve -9 – x + 6.  1313 -9 – x + 6  1313 -9 - 6 – x + 6 - 6  1313 Add 6 to each side. Simplify. -15 – x + 0  1313 Simplify. 45  x or x  45 3131 –(-15) 3131 – 1313 –x To eliminate the coefficient - from the x side, divide both sides by - which is the same as multiplying each side by the reciprocal, - When you divide or multiply both sides by a negative, reverse the direction of the inequality symbol. 1313  1313 3131 Check: -9  – x + 6 1313 -9  – (45) + 6 Substitute 45 for x. 1313 -9 = -9 -9  – (60) + 6 Check the direction of the inequality by substituting x for a value bigger than 45, like 60. 1313 -9  -14 The direction of the sign is correct. “Solving Two-Step Inequalities” (7-5) 3-1)

7. PRE-ALGEBRA Solve 6 – r – 6. < 2323 6 – r – 6 < 2323 6 + 6 – r – 6 + 6 < 2323 Add 6 to each side. Simplify. 12 – r < 2323 Simplify. > –18 r, or r –18 < 3232 –(12) 3232 – 2323 –r Multiply each side by. Reverse the direction of the inequality symbol. 3232 – > Solving Two-Step Inequalities LESSON 7-5 Additional Examples

8. PRE-ALGEBRA Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, what is the greatest number of rides Dale can go on? 25 Inequality4 + 1.5r < Let = number of rides Dale goes on. Words $4 admission + $1.50/ride number of rides is less than or equal to $25 r Solving Two-Step Inequalities LESSON 7-5 Additional Examples

9. PRE-ALGEBRA (continued) The greatest number of rides Dale can go on is 14. 4 + 1.5r 25 < Subtract 4 from each side.4 + 1.5r – 4 25 – 4 < Simplify.1.5r 21 < Divide each side by 1.5. 1.5r 1.5 21 1.5 < Simplify.r 14 < Solving Two-Step Inequalities LESSON 7-5 Additional Examples

10. PRE-ALGEBRA Solve each inequality. 1.14 > 4d – 102. + 8 7 3.32 – 12g < 176 4.8 + 5a 23 > < d < 6k 3 > g > –12 a 3 > – k3k3 Solving Two-Step Inequalities LESSON 7-5 Lesson Quiz