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Solve Inequalities
1© Evergreen Public Schools
7/28/10
©Evergreen Public Schools 2010 2
Linear Inequalities Target 2I can use 5 steps to solve an inequality and graph the solution on a number line.
Explain the inequality for “Edgar’s iTunes”.
Explain the inequality for “Edgar’s iTunes”.
c ≤ 3
What is represented on each number line?
-5 0 5
-5 0 5
-5 0 5
x 2
x 2
x 2
3© Evergreen Public Schools
LaunchLaunchLaunchLaunch
©Evergreen Public Schools 2010 4
Solving Inequalities
3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7 3x = 12
3 3 x = 4
We still need to
figure out what to do with the ≥
sign!
We still need to
figure out what to do with the ≥
sign!
5© Evergreen Public Schools
Step 1: Replace ≥ with = and Solve
Step 1: Replace ≥ with = and Solve
• Where is the middle of the number line?
• Is it here?• Part is on the right. It goes from here to ∞.
• Part is on the left. It goes from here to -∞.
-5 0 5
6© Evergreen Public Schools
• Could the middle be here?
• Part is on the right. It goes from here to ∞.
• Part is on the left. It goes from here to -∞.
-5 0 5
7© Evergreen Public Schools
• Could the middle be here?
So any point divides the number line in two parts.
95 100 105
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Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7
3x = 12
3 3 x = 4
Graph x = 4 on the number line.
Pick a point on either side of 4. Test it in the inequality.
Let’s try x = 5.3(5) + 7 ≥ 19 15 + 7 ≥ 1922 ≥ 19True!
49© Evergreen Public Schools
Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7
3x = 12
3 3 x = 4
Graph x = 4 on the number line.
Pick a point on either side of 4. Test it in the inequality.
Let’s try x = 10.3(10) + 7 ≥ 19 30 + 7 ≥ 1937 ≥ 19True!
410© Evergreen Public Schools
Step 3: Test Points
Step 3: Test Points
Step 4: Represent on number line
Step 4: Represent on number line
Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7
3x = 12
3 3 x = 4
Graph x = 4 on the number line.
Pick a point on either side of 4. Test it in the inequality.
Let’s try x = 3.3(3) + 7 ≥ 19 9 + 7 ≥ 1916 ≥ 19
False!
4
×
11© Evergreen Public Schools
Step 3: Test Points
Step 3: Test Points
Step 4: Represent on number line
Step 4: Represent on number line
Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7
3x = 12
3 3 x = 4
Graph x = 4 on the number line.
Pick a point on either side of 4. Test it in the inequality.
Let’s try x = 0.3(0) + 7 ≥ 19 0 + 7 ≥ 197 ≥ 19
False!
4
××
12© Evergreen Public Schools
Step 3: Test Points
Step 3: Test Points
Step 4: Represent on number line
Step 4: Represent on number line
Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7
3x = 12
3 3 x = 4
Find more solutions.What is a better way to show this on the number line?
So the solution is all numbers greater than or equal to 4.
x ≥ 4
413© Evergreen Public Schools
Step 5: Write the solution
as an inequality.
Step 5: Write the solution
as an inequality.
Work with a Partner
Be prepared to share.
14
#1 Solving Inequalities4x – 1 ≥ 19
4x – 1 = 19 4x – 1 = 19
+1 +1
4 4
x = 5
5
Pick a point to test.
How about x = 4?
4(4) + 1 ≥ 19
16 + 1 ≥ 19 17 ≥ 19
This is not true.
x
15© Evergreen Public Schools
4
4x = 20 4x = 20
Step 1: Replace ≥ with = and Solve
Step 1: Replace ≥ with = and Solve
Step 3: Test Points
Step 3: Test Points
Step 2: Put
or on number line
Step 2: Put
or on number line
Step 4: Represent on number line
Step 4: Represent on number line
Predict what you think the
solution will look like on the number line.
Predict what you think the
solution will look like on the number line.
#1 Solving Inequalities4x – 1 ≥ 19
4x – 1 = 19 4x – 1 = 19
+1 +1
4x = 20 4 4
x = 5
5
Pick a point to test.
How about x = 6?
4(6) + 1 ≥ 19
24 + 1 ≥ 19 25 ≥ 19
This is true.
6x
16© Evergreen Public Schools
4
Step 3: Test Points
Step 3: Test Points
Step 4: Represent on number line
Step 4: Represent on number line
#1 Solving Inequalities4x – 1 ≥ 19
4x – 1 = 19 4x – 1 = 19
+1 +1
4x = 20 4 4
x = 5
5
Pick a point to test.You choose.This half of class pick a point less than 5.This half of class pick a point greater than 5.
6x
17© Evergreen Public Schools
4
#1 Solving Inequalities4x – 1 ≥ 19
4x – 1 = 19 4x – 1 = 19
+1 +1
4x = 20 4 4
x = 5
5
Pick a point to test.
x ≥ 5
6x
18© Evergreen Public Schools
4
What is the best way to describe the solution?
What is the best way to describe the solution?
Was your prediction about the solution correct?
Was your prediction about the solution correct?
Step 5: Write the solution
as an inequality.
Step 5: Write the solution
as an inequality.
Work the next problem by yourself.
Be prepared to share.
19
#2 Solving Inequalities-6x – 3 < 15
20© Evergreen Public Schools 2012
Step 1: Replace ≥ with = and Solve
Step 1: Replace ≥ with = and Solve
Step 3: Test Points
Step 3: Test Points
Step 2: Put
or on number line
Step 2: Put
or on number line
Step 4: Represent on number line
Step 4: Represent on number line
Predict what you think the
solution will look like on the number line.
Predict what you think the
solution will look like on the number line.
Was your prediction about the solution correct?
Was your prediction about the solution correct?
Step 5: Write the solution
as an inequality.
Step 5: Write the solution
as an inequality.
Time to share.
21
©Evergreen Public Schools 2010 22
5
3
12
4
Did you hit the target?
I can use 5 steps to solve an inequality and graph the solution on a number line.
Rate your understanding of the target from 1 to 5.
5 is a bullseye!
©Evergreen Public Schools 2010 23
PracticePractice
Practice 7.3A Solve Inequalities
