# Then/Now You solved one-step and multi-step inequalities. Solve compound inequalities. Solve absolute value inequalities

• View
223

0

Embed Size (px)

### Text of Then/Now You solved one-step and multi-step inequalities. Solve compound inequalities. Solve...

• Then/NowYou solved one-step and multi-step inequalities.Solve compound inequalities.Solve absolute value inequalities.

• Vocabularycompound inequalityintersectionunion

• Concept

• Example 1Solve an And Compound InequalitySolve 10 3y 2 < 19. Graph the solution set on a number line.Method 1Solve separately.Write the compound inequality using the word and. Then solve each inequality.103y 2and3y 2 < 19123y3y < 21 4y y < 74 y < 7

• Example 1Solve an And Compound InequalityMethod 2Solve both together.Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.10 3y 2< 1912 3y< 214 y< 7

• Example 1Solve an And Compound InequalityGraph the solution set for each inequality and find their intersection.Answer:

• Example 1Solve an And Compound InequalityGraph the solution set for each inequality and find their intersection.Answer: The solution set is y | 4 y < 7.

• Example 1What is the solution to 11 2x + 5 < 17?

• Example 1What is the solution to 11 2x + 5 < 17?

• Concept

• Example 2Solve an Or Compound InequalitySolve x + 3 < 2 or x 4. Graph the solution set on a number line.Answer: Solve each inequality separately.

• Example 2Solve an Or Compound InequalitySolve x + 3 < 2 or x 4. Graph the solution set on a number line.Answer: The solution set is x | x < 1 or x 4.Solve each inequality separately.

• Example 2What is the solution to x + 5 < 1 or 2x 6? Graph the solution set on a number line.

• Example 2What is the solution to x + 5 < 1 or 2x 6? Graph the solution set on a number line.

• Example 3Solve Absolute Value InequalitiesA. Solve 2 > |d|. Graph the solution set on a number line.2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0.Answer: All of the numbers between 2 and 2 are less than 2 units from 0.Notice that the graph of 2 > |d| is the same as the graph of d > 2 and d < 2.

• Example 3Solve Absolute Value InequalitiesA. Solve 2 > |d|. Graph the solution set on a number line.2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0.Answer: The solution set is d | 2 < d < 2.All of the numbers between 2 and 2 are less than 2 units from 0.Notice that the graph of 2 > |d| is the same as the graph of d > 2 and d < 2.

• Example 3aA. What is the solution to |x| > 5?

• Example 3aA. What is the solution to |x| > 5?

• Example 3bB. What is the solution to |x| < 5?

• Example 3bB. What is the solution to |x| < 5?

• Concept

• Example 4Solve a Multi-Step Absolute Value InequalitySolve |2x 2| 4. Graph the solution set on a number line.|2x 2| 4 is equivalent to 2x 2 4 or 2x 2 4.Solve each inequality.2x 24or2x 242x62x2x3x1Answer:

• Example 4Solve a Multi-Step Absolute Value InequalitySolve |2x 2| 4. Graph the solution set on a number line.|2x 2| 4 is equivalent to 2x 2 4 or 2x 2 4.Solve each inequality.2x 24or2x 242x62x2x3x1Answer: The solution set is x | x 1 or x 3.

• Example 4What is the solution to |3x 3| > 9? Graph the solution set on a number line.

• Example 4What is the solution to |3x 3| > 9? Graph the solution set on a number line.

• Example 5Write and Solve an Absolute Value InequalityA. JOB HUNTING To prepare for a job interview, Hinda researches the positions requirements and pay. She discovers that the average starting salary for the position is \$38,500, but her actual starting salary could differ from the average by as much as \$2450. Write an absolute value inequality to describe this situation.Let x = the actual starting salary.Answer:

• Example 5Write and Solve an Absolute Value InequalityA. JOB HUNTING To prepare for a job interview, Hinda researches the positions requirements and pay. She discovers that the average starting salary for the position is \$38,500, but her actual starting salary could differ from the average by as much as \$2450. Write an absolute value inequality to describe this situation.Let x = the actual starting salary.Answer:|38,500 x| 2450

• Example 5Write and Solve an Absolute Value InequalityB. JOB HUNTING To prepare for a job interview, Hinda researches the positions requirements and pay. She discovers that the average starting salary for the position is \$38,500, but her actual starting salary could differ from the average by as much as \$2450. Solve the inequality to find the range of Hindas starting salary. | 38,500 x | 2450Rewrite the absolute value inequality as a compound inequality. Then solve for x.245038,500 x 24502450 38,500x 2450 38,50040,950x 36,05040,950x 36,050

• Example 5Write and Solve an Absolute Value InequalityAnswer:

• Example 5Write and Solve an Absolute Value InequalityAnswer: The solution set is x | 36,050 x 40,950. Hindas starting salary will fall within \$36,050 and \$40,950. ##### 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities
Documents ##### 8.4 Solving Two-Step Inequalities - Big Ideas Math Chapter 8 Inequalities 8.4 Lesson You can solve two-step inequalities the same way you solve two-step equations. EXAMPLE 1 Solving
Documents ##### Goal: I can Graph and Solve multi-step linear inequalities. What do we know already? 2.5â€“ Solving Inequalities with Variables on Both Sides Solve inequalities
Documents ##### 2.3 Solving Word Problems. Goals SWBAT solve linear inequalities SWBAT solve linear inequalities SWBAT solve compound inequalities SWBAT solve compound
Documents ##### 5.6 Solve Absolute Value Inequalities You will solve absolute value inequalities. Essential question: How do you solve absolute value inequalities? You
Documents ##### 5.3 Solve Multi-Step Inequalities You will solve multi- step inequalities. Essential question: How do you solve multi-step inequalities? You will learn
Documents ##### LESSON Solve Exponential and Logarithmic Ine 3+-+ML+-+4.8.pdfSolve Exponential and Logarithmic Inequalities ... to solve exponential and logarithmic inequalities. ... STEP 1 Write
Documents ##### Solving Inequalities by Adding or Su Inequalities by...Holt McDougal Algebra 1 Solving Inequalities by Adding or Subtracting Solve one-step inequalities by using addition. Solve one-step
Documents ##### Holt CA Course 1 11-8 Solving Two-Step Inequalities Preview of Grade 7 AF4.1 Solve two-step linear equations and inequalities in one variable over the
Documents ##### 4.4 Solving Two-Step Inequalities - Edl Chapter 4 Inequalities 4.4 Lesson You can solve two-step inequalities in the same way you solve two-step equations. EXAMPLE 1 Solving Two-Step
Documents ##### Regents Review #4 Inequalities and Systems. Simple Inequalities 1)Solve inequalities like you would solve an equation (use inverse operations and properties
Documents ##### Holt McDougal Algebra 1 2-2 Solving Inequalities by Adding or Subtracting Solve one-step inequalities by using addition. Solve one-step inequalities by
Documents Documents