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1.6 Solving Linear Inequalities p. 41

1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

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Page 1: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

1.6 Solving Linear Inequalities

p. 41

Page 2: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Learning Check

• I can solve simple inequalities.

• I can solve compound inequalities.

Page 3: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Inequality SymbolsInequality Symbols

Less than

Greater than

Less than or equal to

Greater than or equal to

Not equal to

Page 4: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Linear Inequality

• Inequality with one variable to the first power.

for example: 2x-3<8

• A solution is a value of the variable that makes the inequality true.

x could equal -3, 0, 1, etc.

Page 5: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Transformations for InequalitiesTransformations for Inequalities

• Add/subtract the same number on each side of an inequality

• Multiply/divide by the same positive number on each side of an inequality

• If you multiply or divide by a negative number, you MUST flip the inequality sign!

Page 6: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Ex: Solve the inequality.

2x-3<8

+3 +3

2x<11

2 2

x<2

11

1373 x

63 x

2x

Flip the sign after dividing by the -3!

Page 7: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Graphing Linear Inequalities

• Remember:

< and > signs will have an open dot o

and signs will have a closed dot

graph of graph of

2

11x 2x

4 5 6 7 -3 -2 -1 0

Page 8: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Example: Solve and graph the solution.

121097 xx

1239 xx321x7

6 7 8 9

Page 9: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Compound Inequality

• An inequality joined by “and” or “or”.

Examples

“and” “or”

think between

think oars on a boat

13 x

-4 -3 -2 -1 0 1 2

4or 2 xx

-3 -2 -1 0 1 2 3 4 5

Page 10: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Example: Solve & graph.

-9 < t+4 < 10

-13 < t < 6

Think between!

-13 6

Page 11: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Last example! Solve & graph. -6x+9 < 3 or -3x-8 > 13

-6x < -6 -3x > 21

x > 1 or x < -7

Flip signs

Think oars

-7 1

Page 12: 1.6 Solving Linear Inequalities p. 41. Learning Check I can solve simple inequalities. I can solve compound inequalities

Assignment