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Linear Inequalities in one variable

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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 Linear Inequalities in one variable

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Transformations for Inequalities Add/subtract the same number on each side of an inequality (as with a linear equation) 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!

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Ex: Solve the inequality 2x-3<8 +3 +3 2x<11 2 2 x< 5.5 Flip the sign when dividing by the -3!

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Recall Graphing a linear Equality with one variable….. x = 4 Notice the circle is closed

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Graphing a linear Inequality with one variable….. x < 4 Notice the circle is open

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Graphing a linear Inequality with one variable….. x > -2 Notice the circle is open

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Graphing a linear Inequality with one variable….. x < 4 Notice the circle is closed

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Graphing a linear Inequality with one variable….. x ≥ -2 Notice the circle is closed

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Will the circle be closed or open? 1.) x = 6 2.) x > 0 3.) x < -3 4.) x > -1 5.) x < 7 1.) closed 2.) open 3.) open 4.) closed 5.) closed

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Solving a linear Inequality p + 5 > 3 p + 5 - 5 > 3 - 5 p > -2 Solve the following linear equation and illustrate your answer graphically

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Solving a linear Inequality 3x < 9 3x / 3 < 9 / 3 x < 3

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Solving a linear Inequality -x < 4 -x/ -1 < 4 / -1 x > -4 The sign flips when you multiply or divide by a negative

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Solving a 3-step inequality 2x - 4 < 4x - 1 2x -4x - 4 < 4x -4x - 1 -2x - 4 < - 1 -2x -4 + 4 < - 1+4 -2x < 3 -2x/-2 < 3/-2

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2x – 4 < 4x – 1 x > -3/2

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Solving a compound inequality To solve a compound inequality, apply the same rules as before – but apply them to both sides of the inequality: -3 < 2x-1 ≤ 5(add 1 to both sides of the inequality) -2 < 2x ≤6 -1 < x ≤ 2(divide through by 2) -2-2 02

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