solve inequalities 1 © evergreen public schools 11/1/2010
TRANSCRIPT
Solve Inequalities
1© Evergreen Public Schools
11/1/2010
I can solve inequalities in one variable.
Explain the inequality for
“Edgar’s etunes”.
Explain the inequality for
“Edgar’s etunes”.
Edgar’s etunes
14.99c ≤ 50.00
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What is represented on each number line?
-5 0 5
-5 0 5
-5 0 5
-5 0 5
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4Inequalities (c) DSchneider
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!
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• 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
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• 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
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• 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 = 4Graph 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 ≥ 19
22 ≥ 19True!
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Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7 3x = 12
3 3 x = 4Graph 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!
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Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7 3x = 12
3 3 x = 4Graph 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 ≥ 19False!
4
×
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Solving Inequalities3x + 7 ≥ 19Solve 3x + 7 = 19 - 7 - 7 3x = 12
3 3 x = 4Graph 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
××
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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
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Work with a Partner
Be prepared to share.
14
#1 Solving Inequalitiesx + 1 + 4x < 11
x + 1 + 4x = 11
1 + 5x = 11
-1 -1
5x = 10 5x = 10 5 5 x = 2
2
Pick a point to test.
How about x = 3?
3 + 1 + 4(3) < 11
3 + 1 + 12 < 11 16 < 11
This is not true.
3x
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#1 Solving Inequalitiesx + 1 + 4x < 11
x + 1 + 4x = 11
1 + 5x = 11
-1 -1
5x = 10 5x = 10 5 5 x = 2
2
Pick another point.
How about x = 0?
0 + 1 + 4(0) < 11
0 + 1 + 0 < 11 1 < 11
This is true.
3x
0
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#1 Solving Inequalitiesx + 1 + 4x < 11
x + 1 + 4x = 11
1 + 5x = 11
-1 -1
5x = 10 5x = 10 5 5 x = 2
2
Pick another point.
How about x = -4?
-4 + 1 + 4(-4) < 11
-4 + 1 – 16 < 11
-19 < 11
This is true.
3x
0
-4
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#1 Solving Inequalitiesx + 1 + 4x < 11
x + 1 + 4x = 11
1 + 5x = 11
-1 -1
5x = 10 5x = 10 5 5 x = 2
2
So, what is the solution?
Draw them on the number line.
All numbers less than or equal to 2.
3x
0
-4
x 2
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Work the next problem by yourself.
Be prepared to share.
19
#2 Solving Inequalities-5(x + 2) < 15
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Time to share.
21
#2 Solving Inequalities-5(x + 2) < 15
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©Evergreen Public Schools 2010 23
Team PracticeTeam Practice
2 - x > 7
Time to share.
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©Evergreen Public Schools 2010 25
PracticePractice
Practice 3.1Solve Inequalities