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

    78

    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.

    Course 3

    10-4 Solving Multistep Inequalities

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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

    Course 3

    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

    Course 3

    10-4 Solving Multistep Inequalities

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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

    Course 3

    10-4 Solving Multistep Inequalities

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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

    Course 3

    10-4 Solving Multistep Inequalities

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    TryThis: Example 2B Continued

    xu 5

    12

    u12x12

    512

    Divide both sides by 12.

    12xu 5

    0 5

    12

    Course 3

    10-4 Solving Multistep Inequalities

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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.

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