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Algebra 1 Compound Inequalities Two inequalities that are joined by the word and or the word or form a compound inequality. You can write the compound inequality x ≥ -5 and x ≤ 7 as -5 ≤ x ≤ 7 “x is greater than or equal to -5 and less than or equal to 7.” OR “x is between -5 and 7, inclusive.”

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Algebra 1 Compound Inequalities And vs. Or And: x must satisfy both inequalities Or: x must satisfy one inequality

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Algebra 1 Compound Inequalities -1 ≤ x < 5 “x is greater than or equal to -1 and x is less than 5.” -1 ≤ x and x < 5 x ≥ -1 and x < 5

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Algebra 1 Compound Inequalities -1 < x ≤ 1 “x is greater than -1 and x is less than or equal to 1.” -1 < x and x ≤ 1 x > -1 and x ≤ 1

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Algebra 1 Lesson 4-5 Write two compound inequalities that represent each situation. Graph the solutions. Compound Inequalities Additional Examples

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Algebra 1 Compound Inequalities Try on your own!! Write a compound inequality and graph the solutions. All real numbers that are greater than or equal to -2 and less than or equal to 4.

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Algebra 1 Solve 5 > 5 – f > 2. Graph the solution. Lesson 4-5 5 – f – 5 > 2 – 5 –f > –3 –3 –1 –f –1 < 5 – 5 > 5 – f – 5 0 > –f 0 –1 –f –1 < 5 – f > 25 > 5 – f f < 30 < f Write the compound inequality as two inequalities joined by and. and Compound Inequalities Additional Examples 0 < f < 3

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Algebra 1 Solve 3 > 2k – 3 > 7. Graph the solution. Lesson 4-5 2k -3 + 3 > 7 + 3 2k > 10 10 2 2k 2 < 3 + 3 > 2k – 3 + 3 6 > 2k 6 2 2k22k2 < 2k – 3 > 73 > 2k – 3 k < 53 < k Write the compound inequality as two inequalities joined by and. and Compound Inequalities Additional Examples 3 < k < 5

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Algebra 1 Compound Inequality Try on your own! Solve the inequality and graph your solution. -3 < 2x -1 < 7

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Algebra 1 Compound Inequalities Envelope Activity You will work in pairs. Each group will get an envelope with a number on the front and each person in that group with a paper numbered 1-8. You will open the envelope you get. Solve the problem and write your work/answer on the piece of paper corresponding to the number on the front of the envelope. Pass the envelope on the group to your left. Keep passing until you get the envelope you started with back.

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Algebra 1 Lesson 4-5 Write an inequality that represents each situation. Graph the solutions. all real numbers that are less than 0 or greater than 3. n 3 Compound Inequalities Additional Examples

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Algebra 1 Try on your own! Write a compound inequality that represents the situation and graph your solution. All real numbers that are less than -3 or greater than 5.

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Algebra 1 Lesson 4-5 Solve the compound inequality 3x + 2 < –7 or –4x + 5 < 1. Graph the solution. 3x + 2 – 2 < –7 – 2 3x < –9 < 3x33x3 –9 3 –4x + 5 – 5 < 1 – 5 –4x < –4 > –4x –4 3x + 2 < –7–4x + 5 < 1or x < –3x > 1 or Compound Inequalities Additional Examples

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Algebra 1 Compound Inequalities Try on your own! Solve the compound inequality and graph the solution. 4v + 3 < -5 or -2v + 7 < 1

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