Download Inequalities

Solving
Inequalities
With Multiple
Steps
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Inequalities
Objective –
To solve inequalities involving two steps.
Easy way
Hard way
2x + 3 > 11
2x + 3 > 11
- Undo
Multiplication
or Division first
- Undo Addition
or Subtraction
first
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1
Inequalities
Hard way
Easy way
-Undo Multiply/Divide 1st -Undo Add/Subtract 1st
2x + 3 > 11
2x + 3 > 11
2
2
-3 -3
2x + 3 > 11
2x > 8
2
2
2
2 2
3
11
x +
>
x>4
2
2
- 23 - 23
x > 8
2
x > 4
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Inequalities
1) Undo the addition or subtraction
operation first, by using inverse
operations.
2) Undo the multiplication or
division second, by using inverse
operations.
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2
Inequalities
REMEMBER: You must always perform the
same operation to both sides of an inequality
to keep it balanced.
To undo an operation, perform its
opposite operation to both sides.
+ → −
− → +
× → ÷
÷ → ×
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Inequalities
1) 2x − 5 ≤ 19
+5 + 5
2x ≤ 24
2
2
x ≤ 12
←
Solid circle
9 10 11 12 13
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3
Inequalities
2) 8x + 1 > 25
−1 − 1
8x > 24
8
8
x>3
Open circle
3
→
4
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Inequalities
3) 15 + x ≥ 6
3
−15
− 15
( 3) x3 ≥ −9 ( 3)
x ≥ −27
Solid circle →
-27
0
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4
Inequalities
4) x − 4 < 3
5
+4 + 4
( 5 ) x5 < 7 ( 5)
x < 35
←
Open circle
-35
0
35
copyright©amberpasillas2010
Inequalities
What Operation Do You Do?
FIRST
SECOND
1. 3x + 8 < 24
Subtract 8
Divide by 3
2. 5x - 10 > 19
Add 10
Divide by 5
3. x - 4 > 20
2
Add 4
Multiply by 2
4. -30 < -5x + 5
Subtract 5
Divide by -5
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5
Inequalities
Think about
what you need to do
to isolate the variable.
Get rid of addition or subtraction
first. Second get rid of
multiplication or division.
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Inequalities
1) 2m + 5 > 19
−5 − 5
2m > 14
2
2
m>7
0
7
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6
Inequalities
2) 7 − 3x ≤ 19
−7
−7
−3x ≤ 12
−3x ≤ 12
−3 − 3
x ≥ −4
-4
0
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Inequalities
3) 5 − 3x > 26
−5
−5
−3x > 21
−3 − 3
x < −7
-14
-7
0
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7
Inequalities
1) Goal: Get the variable alone.
2) Undo operations with their
opposite operation.
3) Always do the same thing to
both sides of an inequality.
4) Easiest to undo add/subtract
before multiply/divide.
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Inequalities
THE END
Take out your study guide!
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8
2 Step Inequality Rules
#12
x
2
+ 6 > 14
-6
-6
x
>8
2
2 ( x2 ) > 2 8
x
Subtract 6 from both sides.
+ 6 and -6 cancel out.
Multiply both sides by 2.
2 divided by 2 cancels out
> 16
Open circle
Get the variable alone.
→
16
18
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#13
2 Step Inequalities
3x + 1 < 4
−1 − 1
3x < 3
3
3
x <1
-1
0
1
2x − 5 ≥ 7
+5 + 5
2x ≥ 12
2
2
x≥6
2
5 6
7
8
copyright©amberpasillas2010
9
#14
Graphing Inequalities
x is less than or
equal to -1
All real numbers
greater than 4
x>4
x ≤ −1
3 4
-3 -2 -1 0
5
6
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10