10-4 Solving Inequalities Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

10-4 Solving Inequalities

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpGraph each number on the number line.

1. 2 2. 7 3. 9

2 3 4 5 6 7 810 9 10


Problem of the Day

Randy purchased a laser tag admission ticket for $5. Each time he plays, he pays an additional $1.50. Write an equation to find out how many games he can play if he has $20 to spend.

5 + 1.5x = 20; Randy can play 10 games.


MA.6.A.3.2 Write, solve, and graph one-…step…inequalities.

Sunshine State Standards


Vocabulary

inequalitysolution of an inequality


An inequality is a statement that two quantities are not equal. The quantitiesare compared by using one of the followingsymbols:

< > ≤ ≥ ≠

An inequality may contain a variable, as in x > 3. A solution of an inequality is any value of the variable that makes the statement true.


Graph the solutions of each inequality on a number line.

Additional Example 1: Graphing Inequalities

2 3 4 5 6 7 8

A. t > 4 Draw an empty circle at 4 to show that 4 is not a solution. Draw an arrow to the right to show that values greater than 4 are solutions.

B. y 11

9 10 11 12 13 14 15

Draw a solid circle at 11 to show that 11 is a solution.Draw an arrow to the left to show values that are equal to or less than 11 are also solutions.


Graph the solution of the inequality b ≤ 4 on a number line.

Check It Out: Example 1

1 2 3 4 5 6 7 8 9 10


Solve and graph each inequality.

Additional Example 2: Solving Inequalities with Addition or Subtraction

5 6 7 8 9 10 11432101–

The solid circle at 8 shows that 8 is a solution.

x – 3 ≥ 5

+ 3 + 3

x – 3 ≥ 5

x ≥ 8

3 is subtracted from x.Add 3 to both sides of theinequality to undo the subtraction.




7654321

5 < x + 3

5 < x + 3-3 - 3 2 < x

or

x > 2



Additional Example 3: Solving Inequalities with Multiplication or Division

5 6 7 8 9 10 11432101–

The empty circle at 4 shows that 4 is not a solution.

8z < 32

8 88z < 32

z < 4

8 is multiplied by z.Divide both sides of theinequality by 8 to undo the multiplication.


Graph the solution of the inequality on a number line.


13 14 15 16 17 18 19

a 4

a4

a 16

> 4

4 ∙ > 4 ∙ 4

10-4 Solving InequalitiesAdditional Example 4: Write an Inequality to Represent

the Situation

Let m represent the amount the friends want to spend.

6 should be less than or equal to

Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

times money need 150

6 ≤x m 150

The inequality 6m ≤ 150 represents the situation.


6m ≤ 1506 6

m ≤ 25

Each friend can spend up to $25.

Divide both sides by 6 to undothe multiplication.

Solve the inequality. 6m ≤ 150.

Additional Example 4A Continued


Additional Example 4 Continued

Check Substitute the input value into the rule.

6(25) ≤ 150 = 150 ≤ 150 check

Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

6(20) ≤ 150 = 120 ≤ 150 check



7 + h > 20

Derek must log at least 20 hours of flight time for a sport pilot certificate. So far, he has logged 7 hours. Write and solve an inequality to describe how much more flight time Derek needs to log.

-7 -7h > 13

Derek must log at least 13 more hours of flight time.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

1. Graph the inequality x > 12 on the number line.


2. 4 + x < 6

3.

11 12 13 14 15 16 17

–3 –2 –1 0 1 2 3x < 2

32 33 34 35 36 37 38y ≥ 32


1. Identify the inequality.

A. x < 1

B. x < 1

C. x > 1

D. x > 1



2. Solve the inequality x + 3 < 9.

A. x < 6

B. x < 12

C. x > 6

D. x > 12



3. Solve the inequality .

A. m < 5

B. m < 5

C. m > 36

D. m > 36


10-4 Solving Inequalities Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

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