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Solving Inequalities

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Solving Inequalities Solving inequalities follows the same procedures as solving equations. There are a few special things to consider with inequalities: We need to look carefully at the inequality sign. We also need to graph the solution set.

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**Review of Inequality Signs**

> greater than < less than greater than or equal less than or equal

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**How to graph the solutions**

> Graph any number greater than. . . open circle, line to the right < Graph any number less than. . . open circle, line to the left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left

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**Solve the inequality: -4 -4 x < 3 x + 4 < 7**

x < 3 Subtract 4 from each side. Keep the same inequality sign. Graph the solution. Open circle, line to the left. 3

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**There is one special case.**

Sometimes you may have to reverse the direction of the inequality sign!! That only happens when you multiply or divide both sides of the inequality by a negative number.

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**Example: -3y > 18 Solve: -3y + 5 >23 -5 -5**

-3y > 18 y < -6 Subtract 5 from each side. Divide each side by negative 3. Reverse the inequality sign. Graph the solution. Open circle, line to the left. -6

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Try these: Solve 2x+3>x+5 Solve - c - 11>23 Solve 3(r-2)<2r+4

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