Compound Inequalities Algebra 1 Two inequalities that are

Compound Inequalities Algebra 1 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. ”

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

Compound Inequalities Algebra 1 -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

Compound Inequalities Algebra 1 -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

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

Compound Inequalities Algebra 1 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.

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

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

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

Compound Inequalities Algebra 1 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.

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

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.

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

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