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Solving Inequalities Pages 142 - 144

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

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Solve the inequality: x + 4 < 7 x + 4 < 7 -4 -4 -4 -4 x 3 x 3 ● Subtract 4 from each side. ● Keep the same inequality sign. ● Graph the solution. ● Open circle, line to the left. 30 <

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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. multiply or divide both sides of the inequality by a negative number.

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Solving an Inequality Solve 5 + y <13 5 + y < 13 Subtract 5 to each side. Write original inequality. Simplify. 5 + y - 5 < 13 - 5 y < 8 To graph y < 8, use an open dot and draw the arrow pointing to the left. 7 345698210 Then graph the solution. Example 1:

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Solving an Inequality Solve a – 3 > -5 a – 3 > -5 Add 3 to each side.. Write original inequality. Simplify. a – 3 + 3 > -5 + 3 a > -2 To graph a > -2 use a closed dot and draw the arrow pointing to the right. Then graph the solution. 2–2–10143–35 Example 2:

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Solve: -3y + 5 >23 -5 -5 -3y > 18 -3 -3 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. 0-6 Example 3:

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Solving Inequalities

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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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