Download - 10-4 Solving Multistep Inequalities
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Warm Up
Solve.
1. 6x+ 36 = 2x
2. 4x 13 = 15 + 5x
3. 5(x 3) = 2x+ 3
4. +x=
x= 9
x= 28
x= 6
Course 3
10-4 Solving Multistep Inequalities
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316 1116x=
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Learn to solvetwo-step inequalities andgraphthe solutions ofan inequalityon a
number line.
Course 3
10-4 Solving Multistep Inequalities
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Solving amultistep inequalityuses the
same inverseoperations as solving amultistepequation. Multiplying ordividing the inequalitybya negative
number reverses the inequalitysymbol.
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Solve and graph.
Additional Example 1A: Solving Multistep
Inequalities
A. 4x+ 1 > 13
4x+ 1 > 13
1 1 Subtract 1 from both sides.4x > 12
4x4
> 124
Divide both sides by 4.
x> 31 2 3 4 5 6 7
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10-4 Solving Multistep Inequalities
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Additional Example 1B: Solving Multistep
Inequalities
B. 7 12
5x+ 2 > 12
2 2 Subtract 2 from both sides.5x > 10
5x5
> 105
Divide both sides by 5.
x> 21 2 3 4 5 6 7
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B. 5
11x
18x+ 8 > 11x 1
8x 8x Subtract 8x from both sides.
8 > 3x 1
93
> 3x3
Add 1 toeach side.
3 >x
-1 0 1 2 3 4 5
+1 +1
9 > 3x
Course 3
10-4 Solving Multistep Inequalities
Divide both sides by 3.
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Solve and graph.
TryThis: Example 2A
A. 15x+30 5x < 10
15x+ 30 5x< 10
30 30 Subtract 30 from both sides.
10x10
< 4010 Divide both sides by 10.
x< 4
-8 -7 -6 -5 -4 -3 -2
10x+ 30 < 10 Combine like terms.
10x < 40
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TryThis: Example 2B
Multiply byLCD, 20.
12x+ 5 u 10
5 5 Subtract 5 from both sides.
12x u 5
B. + u3x
5
1
4
5
10
+ u3x5
14
510
20( + )u
20( )3x
5
1
4
5
10
20( ) + 20( ) u 20 ( )3x514
510
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TryThis: Example 2B Continued
xu 5
12
u12x12
512
Divide both sides by 12.
12xu 5
0 5
12
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TryThis: Example 2C
C. 4x+3 > 8x 1
4x+ 3 > 8x 1
4x 4x Subtract 4x from both sides.
3 > 4x 1
44
> 4x4
Add 1 toeach side.
1 >x
-1 0 1 2 3 4 5
+1 +1
4 > 4x
Course 3
10-4 Solving Multistep Inequalities
Divide both sides by 4.
