Solving TwoStep and 3 4 MultiStep Inequalities Lesson

Solving Two-Step and 3 -4 Multi-Step Inequalities Lesson Objective: I will be able to … • Solve inequalities that contain more than one operation Language Objective: I will be able to … • Read, write, and listen about vocabulary, key concepts, and examples Holt Algebra 1

Solving Two-Step and 3 -4 Multi-Step Inequalities Example 1: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. Page 23 8 – 3 y ≥ 29 – 8 Since 8 is added to – 3 y, subtract 8 from both sides to undo the addition. – 3 y ≥ 21 Since y is multiplied by – 3, divide both sides by – 3 to undo the multiplication. Change ≥ to ≤. y ≤ – 7 – 10 – 8 – 6 – 4 – 2 Holt Algebra 1 0 2 4 6 8 10

Solving Two-Step and 3 -4 Multi-Step Inequalities Your Turn 1 Page 24 Solve the inequality and graph the solutions. – 12 ≥ 3 x + 6 – 6 Since 6 is added to 3 x, subtract 6 from both sides to undo the addition. – 18 ≥ 3 x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. – 6 ≥ x or x ≤ -6 – 10 – 8 – 6 – 4 – 2 Holt Algebra 1 0 2 4 6 8 10

Solving Two-Step and 3 -4 Multi-Step Inequalities Example 2: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. – 4(2 – x) ≤ 8 Page 24 − 4(2 – x) ≤ 8 − 4(2) − 4(−x) ≤ 8 – 8 + 4 x ≤ 8 +8 +8 4 x ≤ 16 Distribute – 4 on the left side. Since – 8 is added to 4 x, add 8 to both sides. Since x is multiplied by 4, divide both sides by 4 to undo the multiplication. x≤ 4 – 10 – 8 – 6 – 4 – 2 Holt Algebra 1 0 2 4 6 8 10

Solving Two-Step and 3 -4 Multi-Step Inequalities Page 25 Example 3: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions: Multiply both sides by 6, the LCD of the fractions. Distribute 6 on the left side. 4 f + 3 > 2 – 3 4 f > – 1 Since 3 is added to 4 f, subtract 3 from both sides to undo the addition. Since f is multiplied by 4, divide both sides by 4 to undo the multiplication. 0 Holt Algebra 1

Solving Two-Step and 3 -4 Multi-Step Inequalities Example 4: Consumer Application Page 26 To rent a certain vehicle, Rent-A-Ride charges $55. 00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38. 00 per day plus $0. 20 per mile. For what number of miles in the cost at Rent-A-Ride less than the cost at We Got Wheels? Let m represent the number of miles. The cost for Rent. A-Ride should be less than that of We Got Wheels. Cost at Rent-ARide must be less than 55 < Holt Algebra 1 daily cost at We Got Wheels 38 plus + $0. 20 per mile 0. 20 times # of miles. m

Solving Two-Step and 3 -4 Multi-Step Inequalities Example 4 Continued 55 < 38 + 0. 20 m Since 38 is added to 0. 20 m, subtract 55 < 38 + 0. 20 m 38 from both sides to undo the addition. – 38 17 < 0. 20 m Since m is multiplied by 0. 20, divide both sides by 0. 20 to undo the multiplication. 85 < m Rent-A-Ride costs less when the number of miles is more than 85. Holt Algebra 1

Solving Two-Step and 3 -4 Multi-Step Inequalities Classwork Assignment #5 • Holt 3 -4 #5, 12, 15 Holt Algebra 1