Solving TwoStep and 3 4 MultiStep Inequalities Objective
Solving Two-Step and 3 -4 Multi-Step Inequalities Objective Solve inequalities that contain more than one operation. Holt Algebra 1
Solving Two-Step and 3 -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 Holt Algebra 1 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
Solving Two-Step and 3 -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 Algebra 1 0 2 4 6 8 10
Solving Two-Step and 3 -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 Algebra 1 0 2 4 6 8 10
Solving Two-Step and 3 -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 Holt Algebra 1 – 12 – 8 – 4 0
Solving Two-Step and 3 -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 Algebra 1 – 16 – 12 – 8 – 4 0
Solving Two-Step and 3 -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 Algebra 1 0 2 4 6 8 10
Solving Two-Step and 3 -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 Algebra 1 0 2 4 6 8 10
Solving Two-Step and 3 -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 Holt Algebra 1 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
Solving Two-Step and 3 -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 Algebra 1 0 2 4 6 8 10
Solving Two-Step and 3 -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 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 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 Algebra 1
Solving Two-Step and 3 -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 Algebra 1
Solving Two-Step and 3 -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 Algebra 1
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