Solving Multi-Step Inequalities Section 2.4. Warm Up Solve each equation. 1. 2x – 5 = –17 2. Solve each inequality and graph the solutions. 4. 3. 5 <

Slides:



Advertisements
Similar presentations
Warm Up Solve each equation. 1. 2x = 7x x = –3
Advertisements

Warm Up Lesson Presentation Lesson Quiz.
Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14
Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14
Objective Solve inequalities that contain more than one operation.
Multi-Step Inequalities
Holt McDougal Algebra Solving Inequalities with Variables on Both Sides Solve inequalities that contain variable terms on both sides. Objective.
Chapter 2 Section 4 Copyright © 2011 Pearson Education, Inc.
Let w represent an employee’s wages.
Section 2.2 More about Solving Equations. Objectives Use more than one property of equality to solve equations. Simplify expressions to solve equations.
Holt McDougal Algebra 1 Solving Two-Step and Multi-Step Equations Warm Up Evaluate each expression –3(–2) 2. 3(–5 + 7) – 4(7 – 5) Simplify.
Solving Multi-Step Equations by Clearing the Fractions.
Graph each inequality. Write an inequality for each situation. 1. The temperature must be at least –10°F. 2. The temperature must be no more than 90°F.
Multi-Step Inequalities
Algebra 1 Chapter 3 Section Solving Inequalities With Variables on Both Sides Some inequalities have variable terms on both sides of the inequality.
Warm Up Lesson Presentation Lesson Quiz.
Chapter 3 - Inequalities Algebra I. Table of Contents Graphing and Writing Inequalities Solving Inequalities by Adding or Subtracting.
Objective: To solve multi-step inequalities Essential Question: How do I solve multi-step inequality? Example #1 : solving multi-step inequalities 2x −
Holt McDougal Algebra Solving Two-Step and Multi-Step Inequalities Solve inequalities that contain more than one operation. Objective.
Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14
Solving Two-Step and 3.1 Multi-Step Equations Warm Up
Chapter Solving two step inequalities.  Matt has 4 more hats than Aaron and half as many hats as Michael. If the three together have 24 hats, how.
One Step Equations and Inequalities Review
Solve inequalities that contain more than one operation.
Solving Two-Step and Multi-Step Equations Warm Up Lesson Presentation
Warm-up #12 ab 1 3x  1814x  x > 32-5x < x  -3 7x > x < x  -24.
CONFIDENTIAL 1 Algebra1 Solving Two-Step and Multi-Step Inequalities.
3-4 Solving Two-Step and Multi-Step Inequalities Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.
3. 3 Solving Equations Using Addition or Subtraction 3
Solving Multi-Step Inequalities
Multi-Step Inequalities
Multi-Step Inequalities
Solving Multi-Step Equations by Clearing the Fractions
Multi-Step Inequalities
Objective 3.6 solve multi-step inequalities.
Preview Warm Up California Standards Lesson Presentation.
Find the least common multiple for each pair.
Solving Equations and Inequalities
Objective Solve equations in one variable that contain more than one operation.
Solving Equations with the Variable on Both Sides
10 Real Numbers, Equations, and Inequalities.
Solving Inequalities with Variables on Both Sides
Multi-Step Inequalities
Objective Solve equations in one variable that contain variable terms on both sides.
Find the least common multiple for each pair.
Multi-Step Inequalities
Solving Two-Step and Multi -Step Inequalities
DO NOW: Write homework in your agenda
Lesson Objective: I will be able to …
Example 1A: Solving Multi-Step Inequalities
Multi-Step Inequalities
Objective Solve equations in one variable that contain more than one operation.
Example 1A: Solving Inequalities with Variables on Both Sides
Objective Solve inequalities that contain variable terms on both sides.
Objective Solve equations in one variable that contain variable terms on both sides.
Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14
Multi-Step Inequalities
Objective Solve equations in one variable that contain more than one operation.
Multi-Step Inequalities
Multi-Step Inequalities
Objective Solve equations in one variable that contain more than one operation.
Objective Solve inequalities that contain more than one operation.
Multi-Step Inequalities
Algebra 1 10/17/16 EQ: How do I solve 2 and multi step inequalities?
Multi-Step Inequalities
Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14
Multi-Step Inequalities
Multi-Step Inequalities
If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before.
Multi-Step Inequalities
Presentation transcript:

Solving Multi-Step Inequalities Section 2.4

Warm Up Solve each equation. 1. 2x – 5 = –17 2. Solve each inequality and graph the solutions < t + 9 –6 14 t > –4 a ≤ –8

Solve the inequality and graph the solutions b > 61 –45 2b > 16 b > Since 45 is added to 2b, 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 – 3y ≥ 29 –8 –3y ≥ 21 y ≤ –7 Since 8 is added to –3y, subtract 8 from both sides to undo the addition. Since y is multiplied by –3, divide both sides by –3 to undo the multiplication. Change ≥ to ≤. –10 –8 –6–4 – –7 Solve the inequality and graph the solutions.

–12 ≥ 3x + 6 – 6 –18 ≥ 3x –6 ≥ x Since 6 is added to 3x, subtract 6 from both sides to undo the addition. Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. –10 –8 –6–4 –

Solve the inequality and graph the solutions. x < –11 –5 x + 5 < –6 –20 –12–8–4 –16 0 –11 Since x is divided by –2, multiply both sides by –2 to undo the division. Change > to <. Since 5 is added to x, subtract 5 from both sides to undo the addition.

Solve the inequality and graph the solutions. 1 – 2n ≥ 21 –1 –2n ≥ 20 n ≤ –10 Since 1 – 2n is divided by 3, multiply both sides by 3 to undo the division. Since 1 is added to –2n, 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 ≤. –10 –20 –12–8–4 –16 0

Solve the inequality and graph the solutions. 4f + 3 > 2 –3 4f > –1 Multiply both sides by 6, the LCD of the fractions. Distribute 6 on the left side. Since 3 is added to 4f, subtract 3 from both sides to undo the addition.

Solve the inequality and graph the solutions (x + 4) > x + 8 > 3 2x + 11 > 3 – 11 2x > –8 x > –4 Distribute 2 on the left side. Combine like terms. Since 11 is added to 2x, subtract 11 from both sides to undo the addition. Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. –10 –8 –6–4 –

Solve the inequality and graph the solutions. 5 < 3x – < 3x Multiply both sides by 8, the LCD of the fractions. Distribute 8 on the right side. Since 2 is subtracted from 3x, add 2 to both sides to undo the subtraction.

Example 3 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-A- Ride must be less than daily cost at We Got Wheels plus $0.20 per mile times # of miles. 55 <  m

85 < m Since 38 is added to 0.20m, subtract 38 from both sides to undo the addition. Since m is multiplied by 0.20, divide both sides by 0.20 to undo the multiplication. Rent-A-Ride costs less when the number of miles is more than < m –38 55 < m 17 < 0.20m

Example 4 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 plus second test score divided by number of scores is greater than or equal to total score (95 + x) x)  2 ≥ 90

The score on the second test must be 85 or higher. Since 95 is added to x, subtract 95 from both sides to undo the addition x ≥ 180 –95 x ≥ 85 Since 95 + x is divided by 2, multiply both sides by 2 to undo the division.