 #  Compound Inequality › Two inequalities that are joined by the word and or the word or.

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 Compound Inequality › Two inequalities that are joined by the word and or the word or

› Let’s say you have the inequalities:  X ≥ -5 AND X ≤ 7 › You can join them together as a COMPOUND INEQUALITY by writing it this way:  -5 ≤ X ≤ 7

Smaller Number Inequality Sign Variable Inequality Sign Larger Number

 Use a number line to graph inequalities. › Graph -5 ≤ X ≤ 7 › The black shaded portion represents the compound inequality above -7 -6 -5 -4 -3 -2 –1 0 1 2 3 4 5 6 7 8

 All real numbers that are AT LEAST -2 and AT MOST 4. x ≤ 4 and x ≥ -2 -2 ≤ x ≤ 4

 Temperatures that are ABOVE 32 degrees but NOT AS HIGH AS 40 degrees. t > 32 and t < 40 32 < t < 40

 Solve -4 < x – 5 ≤ -1 First step: Write the compound inequality as TWO inequalities joined by AND -4 < x – 5 AND x – 5 ≤ -1

 Second Step: › Solve each inequality as you normally would.  -4 < x – 5 AND x – 5 ≤ -1 +5 + 5 +5 +5 1 < x AND x ≤ 4 Solution: 1 < x ≤ 4

 -6 ≤ 3x < 15  -3 < 2x – 1 < 7  7 < -3x + 1 ≤ 13

 A solution of a compound inequality joined by the word or is any number that makes EITHER inequality true.  Example: › All real numbers that are less than -3 OR greater than 7. X 7

 Use a number line to graph inequalities. › Graph x 7 -7 -6 -5 -4 -3 -2 –1 0 1 2 3 4 5 6 7 8

 Solve 4v + 3 < -5 OR -2v + 7 < 1 First step: Write the compound inequality as TWO inequalities joined by OR 4v + 3 < -5 OR -2v + 7 < 1

 Second Step: › Solve each inequality as you normally would.  4v + 3 < –5 OR -2v + 7 < 1 - 3 -3 - 7 -7 4v < -8 -2v < -6 ÷ 4 ÷ 4 ÷ -2 ÷ -2 v 3 - 2 3

 Look for these WORD CLUES to help you determine which inequality symbol to use. ><≥≤ Is more than Is greater than Is larger than Above Is less than Is smaller than Below Minimum At least No less than No smaller than Maximum At most No greater than No more than

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