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1.6 Solving Linear Inequalities

1.6 Solving Linear Inequalities. p. 41. Inequality Symbols. Less than. Not equal to. Less than or equal to. Greater than or equal to. Greater than. Linear Inequality. Inequality with one variable to the first power. for example: 2x-3<8

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1.6 Solving Linear Inequalities

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  1. 1.6 Solving Linear Inequalities p. 41

  2. Inequality Symbols Less than Not equal to Less than or equal to Greater than or equal to Greater than

  3. 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.

  4. Transformations 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 MUSTflip the inequality sign!

  5. Ex: Solve the inequality. 2x-3<8 +3 +3 2x<11 2 2 x< Flip the sign after dividing by the -3!

  6. Graphing Linear Inequalities • Remember: < and > signs will have an open dot o and signs will have a closed dot graph of graph of 4 5 6 7 -3 -2 -1 0

  7. Example: Solve and graph the solution. 6 7 8 9

  8. Compound Inequality • An inequality joined by “and” or “or”. Examples “and” “or” think between think oars on a boat -3 -2 -1 0 1 2 3 4 5 -4 -3 -2 -1 0 1 2

  9. Example: Solve & graph. -9 < t+4 < 10 -13 < t < 6 Think between! -13 6

  10. 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

  11. Assignment

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