warm up solve each equation. 1. –5 a = 30 2
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Warm Up Solve each equation. 1. –5 a = 30 2. –10. –6. 3. 4. Graph each inequality. 5. x ≥ –10. 6. x < –3. Lesson 3.3 Solving Inequalities by Multiplying or Dividing. Less than or equal to. Less than. ≤. . ≥. - PowerPoint PPT PresentationTRANSCRIPT
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Warm UpSolve each equation. 1. –5a = 30 2.
Graph each inequality.
5. x ≥ –10
6. x < –3
–6 –10
3. 4.
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Lesson 3.3Solving Inequalities by Multiplying or Dividing
≥
<
>
≤Less than or equal to
greater than greater than or equal to
Less than
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Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
California Standards
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Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
Notice colored in circles
≤ is less than or equal to
≥ is greater than or equal to
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Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
Notice
open circles
< is less than
> is greater than
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Solving Inequalities Using MultiplicationSolving Inequalities Using Multiplication x -2
3
x -2 3 x -6
Translation: x divided by 3 is greater than or equal
to negative 2.
The opposite of divided by 3 is Multiplying by 3.
What you do on one side you do on the other!
3 • • 3
Graph
-2 0 4-4-6
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Solving Inequalities Using DivisionSolving Inequalities Using Division
3x ≤ 12
3x ≤ 12 3
Translation: 3times x is less than or equal to 12.
The opposite of multiplying by 3 is divided by 3.
What you do on one side you do on the other!31
Graph
0 2 4-2-4
x ≤ 4
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Solve the inequality. Then Solve the inequality. Then graph the solution.graph the solution.
k210)2 3
6)1r
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Multiplying and Dividing Inequalities by aMultiplying and Dividing Inequalities by a
Negative NumberNegative Number Solve the
inequality. 12 > -3m
4 < m
Step1: solve for m -divide by -3
Step 2: reverse the inequality symbol-3 -3
<12 > -3m
When multiplying or dividing by a negative number reverse the inequality symbol.
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Multiplying and Dividing Inequalities by a Negative Number
Solve the inequality. k < -3
Step1: solve for k -Multiply by -2
Step 2: reverse the inequality symbol>
-2.
When multiplying or dividing by a negative number reverse the inequality symbol.
-2
.-2
k > 6
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Tell whether the operation reverses Tell whether the operation reverses
the sign of the inequality.the sign of the inequality.
1) Multiply each side by -1
2) Multiply each side b
3) Divide each side by 4.
4) Divide each side by -5.
1
4
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You try: Solve the InequalitiesYou try: Solve the Inequalities
1) 2x 16
4)7 m4
2)x
510
3) 4k 12
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Additional Example: Application
$4.30 times number of tubes is at most $20.00.
4.30 • p ≤ 20.00
Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?
Let p represent the number of tubes of paint that Jill can buy.
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4.30p ≤ 20.00
p ≤ 4.65…
Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change.
Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint.
Additional Example ContinuedJill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?
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Lesson QuizSolve each inequality and graph the solutions.
1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6
3. x > 20 4. x ≥ 6
5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy?0, 1, 2, 3, 4, 5, 6, or 7 shirts