Solving TwoStep and MultiStep Inequalities Warm Up Lesson

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Solving Two-Step and Multi-Step Inequalities Warm Up Lesson Presentation Lesson Quiz Holt 1 Algebra

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

Solving Two-Step and Multi-Step Inequalities Warm Up Solve each equation. 1. 2 x –

Solving Two-Step and Multi-Step Inequalities Warm Up Solve each equation. 1. 2 x – 5 = – 17 – 6 14 2. Solve each inequality and graph the solutions. 3. 5 < t + 9 t > – 4 4. a ≤ – 8 Holt Mc. Dougal Algebra 1

Solving Two-Step and Multi-Step Inequalities Objective Solve inequalities that contain more than one operation.

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

Solving Two-Step and Multi-Step Inequalities that contain more than one operation require more than

Solving Two-Step and Multi-Step Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time. Holt Mc. Dougal Algebra 1

Solving Two-Step and Multi-Step Inequalities Example 1 A: Solving Multi-Step Inequalities Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Example 1 B: Solving Multi-Step Inequalities Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 1 a Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 1 b Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 1 c Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities To solve more complicated inequalities, you may first need

Solving Two-Step and Multi-Step Inequalities To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides by using the order of operations, combining like terms, or using the Distributive Property. Holt Mc. Dougal Algebra 1

Solving Two-Step and Multi-Step Inequalities Example 2 A: Simplifying Before Solving Inequalities Solve the

Solving Two-Step and 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 Multi-Step Inequalities Example 2 B: Simplifying Before Solving Inequalities Solve the

Solving Two-Step and 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 Multi-Step Inequalities Example 2 C: Simplifying Before Solving Inequalities Solve the

Solving Two-Step and 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 Multi-Step Inequalities Example 2 C Continued 4 f > – 1

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 2 a Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 2 b Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 2 c Solve the inequality

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 2 c Continued Solve the

Solving Two-Step and 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 Multi-Step Inequalities Example 3: Application To rent a certain vehicle, Rent-A-Ride

Solving Two-Step and 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 Multi-Step Inequalities Example 3 Continued 55 < 38 + 0. 20

Solving Two-Step and 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 Multi-Step Inequalities Example 3 Continued Check the endpoint, 85. 55 =

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 3 The average of Jim’s

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 3 Continued Since 95 +

Solving Two-Step and 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 Multi-Step Inequalities Check It Out! Example 3 Continued Check the end

Solving Two-Step and 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 Multi-Step Inequalities Lesson Quiz: Part I Solve each inequality and graph

Solving Two-Step and 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 Multi-Step Inequalities Lesson Quiz: Part II 5. A video store has

Solving Two-Step and 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