graph & solve inequalities

8/10/2019 Graph & Solve Inequalities

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6.5 Inequalities


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Bumper Cars You must be at least 130cmtall to

ride the bumper cars. This can be represented

by the inequality h130.

In the Real World

Solving Inequalities6.5


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The solution of an inequalityis the set of numbers that you can substitute forthe variable to make the inequality true.

An inequalityis a mathematical sentence formed

by placing an inequality symbol between two

expressions.

Bumper Cars You must be at least 130cmtall to

ride the bumper cars. This can be represented

by the inequality h130.

In the Real World

The graph of an inequalityin one variable is the set of points on a number

line that represents the solution of the inequality.

Solving Inequalities65.


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Graphing Inequalities

EXAMPLE 1x< 2 All numbers less than 2

13 2 1 0 324 4



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x1 All numbers less

than or equal to

1

13 2 1 0 324 4

1

3

2

1 0 32

4 4



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x 1 All numbers less

than or equal to

1

x> 0 All numbers greater than 0

13 2 1 0 324 4

1

3

2

1 0 32

4 4

13 2 1 0 324 4



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x 1 All numbers less

than or equal to

1

x> 0 All numbers greater than 0

x 2 All numbers greater

than or equal to

2

13 2 1 0 324 4

1

3

2

1 0 32

4 4

13 2 1 0 324 4

1

3

2

1 0 32

4 4



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Solving Inequalities

Equivalent inequalitiesare inequalities that have the same solution. You

can produce an equivalent inequality in the following ways:

Add or subtract the same number on each side.

Multiply or divide each side by the samepositivenumber.

1 < 3 2 < 6Multiply each side by 2.

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Solving an Inequality

EXAMPLE 2Solve d2 1.

d2 1

Add 2to each side.

Write inequality.

Simplify.

d2 + 2 1 + 2

d 3

To graph d3,use a closed dot and

draw the arrow pointing to the left.

22 1 0 1 433 5

Then graph the solution.

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EXAMPLE 2Solve d2 1.

d2 1

Add 2to each side.

Write original inequality.

Simplify.

Write original equation.

Substitute 0for d.

Solution checks.

d2 + 2 1 +2

d3

To graph d3,use a closed dot and

draw the arrow pointing to the left.

CHECK To check the solution

d3,choose any number less

than or equal to 3to substitute for

d. The check below uses d= 0.

d2 1

2 1

22 1 0 1 433 5


02 1?

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EXAMPLE 4Solve a 3 > -5

a 3 > -5

Add 3 to each side..


Simplify.

a 3 3> -5 3

a > -2

To graph a > -2use a closed dot anddraw the arrow pointing to the right.


65.

22 1 0 1 433 5


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EXAMPLE 5Solve 3 t > 12

3 t > 12

Divide each side by 3..


Simplify.

3 t > 12

t > 4

To graph t > 4use an open dot anddraw the arrow pointing to the right.


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84 5 6 7 1093 11

3 3


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EXAMPLE 6Solve 3x 5 < 23

3x 5 < 23

Subtract 5 on each side


Simplify.

3x 5 < 23

3x < 18

To graph x < 6use an open dot anddraw the arrow pointing to the left.


65.

84 5 6 7 1093 11

5 5

x < 6 Divide both sides by3 and simplify

Assignment: p. 248 9 - 22

graph & solve inequalities

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