Solving TwoStep and 2 4 MultiStep Inequalities Warm

Solving Two-Step and 2 -4 Multi-Step Inequalities Warm Up Lesson Presentation Lesson Quiz Holt 1 Algebra 1 Holt. Algebra Mc. Dougal

Solving Two-Step and 2 -4 Multi-Step Inequalities Objective Solve inequalities that contain more than one operation. Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 1 A: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 45 + 2 b > 61 – 45 2 b > 16 b>8 0 2 4 6 Since 45 is added to 2 b, subtract 45 from both sides to undo the addition. Since b is multiplied by 2, divide both sides by 2 to undo the multiplication. 8 10 12 14 16 18 20 Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 1 B: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 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 Mc. Dougal Algebra 1 0 2 4 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 1 a 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 – 10 – 8 – 6 – 4 – 2 Holt Mc. Dougal Algebra 1 0 2 4 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 1 b Solve the inequality and graph the solutions. Since x is divided by – 2, multiply both sides by – 2 to undo the division. Change > to <. x + 5 < – 6 – 5 Since 5 is added to x, subtract 5 from both sides to undo the addition. x < – 11 – 20 – 16 – 12 Holt Mc. Dougal Algebra 1 – 8 – 4 0

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 1 c Solve the inequality and graph the solutions. 1 – 2 n ≥ 21 – 1 – 2 n ≥ 20 Since 1 – 2 n is divided by 3, multiply both sides by 3 to undo the division. Since 1 is added to – 2 n, subtract 1 from both sides to undo the addition. Since n is multiplied by – 2, divide both sides by – 2 to undo the multiplication. Change ≥ to ≤. n ≤ – 10 – 20 Holt Mc. Dougal Algebra 1 – 16 – 12 – 8 – 4 0

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 2 A: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. 2 – (– 10) > – 4 t 12 > – 4 t Combine like terms. Since t is multiplied by – 4, divide both sides by – 4 to undo the multiplication. Change > to <. – 3 < t (or t > – 3) – 3 – 10 – 8 – 6 – 4 – 2 Holt Mc. Dougal Algebra 1 0 2 4 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 2 B: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. – 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 Mc. Dougal Algebra 1 0 2 4 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 2 C: 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 Holt Mc. Dougal Algebra 1 Since 3 is added to 4 f, subtract 3 from both sides to undo the addition.

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 2 C Continued 4 f > – 1 Since f is multiplied by 4, divide both sides by 4 to undo the multiplication. 0 Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 2 a Solve the inequality and graph the solutions. 2 m + 5 > 52 2 m + 5 > 25 – 5>– 5 2 m > 20 m > 10 0 2 4 6 Simplify 52. Since 5 is added to 2 m, subtract 5 from both sides to undo the addition. Since m is multiplied by 2, divide both sides by 2 to undo the multiplication. 8 10 12 14 16 18 20 Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 2 b Solve the inequality and graph the solutions. 3 + 2(x + 4) > 3 Distribute 2 on the left side. 3 + 2(x + 4) > 3 3 + 2 x + 8 > 3 Combine like terms. Since 11 is added to 2 x, subtract 11 from both sides to undo the addition. 2 x + 11 > 3 – 11 2 x > – 8 Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. x > – 4 – 10 – 8 – 6 – 4 – 2 Holt Mc. Dougal Algebra 1 0 2 4 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 2 c Solve the inequality and graph the solutions. Multiply both sides by 8, the LCD of the fractions. Distribute 8 on the right side. 5 < 3 x – 2 +2 +2 7 < 3 x Holt Mc. Dougal Algebra 1 Since 2 is subtracted from 3 x, add 2 to both sides to undo the subtraction.

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 2 c Continued Solve the inequality and graph the solutions. 7 < 3 x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. 0 2 4 Holt Mc. Dougal Algebra 1 6 8 10

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 3: Application 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 is 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 Mc. Dougal Algebra 1 daily cost at We Got Wheels 38 plus + $0. 20 per mile 0. 20 times # of miles. m

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 3 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 Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Example 3 Continued Check the endpoint, 85. 55 = 38 + 0. 20 m Check a number greater than 85. 55 < 38 + 0. 20 m 55 38 + 0. 20(85) 55 < 38 + 0. 20(90) 55 55 38 + 17 55 < 38 + 18 55 < 56 Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 3 The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What grades can Jim get on his second test to make an A in the class? Let x represent the test score needed. The average score is the sum of each score divided by 2. First test score (95 plus second test score + Holt Mc. Dougal Algebra 1 x) divided by number of scores 2 is greater than or equal to ≥ total score 90

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 3 Continued Since 95 + x is divided by 2, multiply both sides by 2 to undo the division. 95 + x ≥ 180 – 95 Since 95 is added to x, subtract 95 from both sides to undo the addition. x ≥ 85 The score on the second test must be 85 or higher. Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Check It Out! Example 3 Continued Check the end point, 85. Check a number greater than 85. 90 90 Holt Mc. Dougal Algebra 1 90. 5 ≥ 90

Solving Two-Step and 2 -4 Multi-Step Inequalities Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 – 2 x ≥ 21 x ≤ – 4 2. – 11 + 2 < 3 p p > – 3 3. 23 < – 2(3 – t) t>7 4. Holt Mc. Dougal Algebra 1

Solving Two-Step and 2 -4 Multi-Step Inequalities Lesson Quiz: Part II 5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1. 25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A? more than 12 movies Holt Mc. Dougal Algebra 1