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10-4 Solving Inequalities
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
10-4 Solving Inequalities
Warm UpGraph each number on the number line.
1. 2 2. 7 3. 9
2 3 4 5 6 7 810 9 10
10-4 Solving Inequalities
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.
10-4 Solving Inequalities
MA.6.A.3.2 Write, solve, and graph one-…step…inequalities.
Sunshine State Standards
10-4 Solving Inequalities
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.
10-4 Solving Inequalities
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.
10-4 Solving Inequalities
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
10-4 Solving Inequalities
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.
10-4 Solving Inequalities
Solve and graph each inequality.
Check It Out: Example 2
7654321
5 < x + 3
5 < x + 3-3 - 3 2 < x
or
x > 2
10-4 Solving Inequalities
Solve and graph each inequality.
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.
10-4 Solving Inequalities
Graph the solution of the inequality on a number line.
Check It Out: Example 3
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.
10-4 Solving Inequalities
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
10-4 Solving Inequalities
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
10-4 Solving Inequalities
Check It Out: Example 4
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.
10-4 Solving Inequalities
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
10-4 Solving Inequalities
Lesson Quiz
1. Graph the inequality x > 12 on the number line.
Solve and graph each inequality.
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
10-4 Solving Inequalities
1. Identify the inequality.
A. x < 1
B. x < 1
C. x > 1
D. x > 1
Lesson Quiz for Student Response Systems
10-4 Solving Inequalities
2. Solve the inequality x + 3 < 9.
A. x < 6
B. x < 12
C. x > 6
D. x > 12
Lesson Quiz for Student Response Systems