6 2solving Inequalities
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Solving Multi-stepInequalities
Ch 6 lesson 2
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Review
• Solve for m
3 900x
19
3x
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3 900x
3 900
3 3x
1 300x
300x
19
3x
3 19 3
1 3x
1 27x
27x
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What’s the Deal?
In today’s lesson we will solve multi-step inequalities and graph them using a number line.
These will be similar to the multi-step equations that we worked through n Unit Three.
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Back to Unit Three, But with an Inequality
9x
This should look similar to your first equation. The greater than sign replaces the equal sign.
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1 9x
9x
Work the algebra problem just like you would with the = sign
9x Divide negative 1 from
both sides
The answer shows that any number greater than 9 will make a true statement.
1 9
1 1
x
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Fun with graphing
We can use a number line to show all the numbers that work for m.
9x
-6 -4 -2 0 +2 +4 +6
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Graph x >9• Start with the number line
• Put an open circle on 5.85
• Fill in everything to greater than 5.85.
-6 -4 -2 0 +2 +4 +6
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OR Graph x >9• Start with the number line• You only need to mark 9• Put an open circle on 9• Fill in everything to greater than 9.
9
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10x
Work the multi-step algebra problem just like you would with the = sign, then graph.
3 (2 6 ) 28x x
3 2 6 28x x
2 3 28x 2 2
1 10x
3 30
3 3x
-10
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10x
Another twist to algebra
1 10x
3 30
3 3x
-10
Whenever you multiply or divide BY A NEGATIVE NUMBER you must
flip the inequality.
10x
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Let’s check our work
10x-10
Pick an number from the graphed answer set to see if this works.
+10
3(10) (2 6(10) 28
30 (62) 28
32 28
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Try one. Solve for x and graph the inequality.
c + 7 < -11
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Solutionc + 7 – 7 < -11 – 7
c + 0 < -18
-18
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Greater than or equal to has a closed circle.
Graph 3x
-3
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Check your work.Could 10 be a solution for x?
3x-3
10 3Ten is part of the graphed solution
+10
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Summary
• Solving inequalities is similar to solving other algebraic equations.
• Use open circles for greater than (>) or less than (<).
• Use closed circles to show less-than-or equal-to and greater-than-or-equal-to.
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Assignment: pg. 280 :15 – 29; 36-37; 43, 45