BELLWORK Solve the inequalities then graph the solution

BELL-WORK Solve the inequalities, then graph the solution. 1. 12 x – 3 x + 11 ≥ 4 x – (17 – 9 x) 9 x + 11 ≥ 13 x – 17 28 ≥ 4 x x≤ 7 2. -8 ≤ 2 x – 4 ≤ 4 -4 ≤ 2 x ≤ 8 -2 ≤ x ≤ 4

Absolute Value Inequalities Absolute value inequalities are inequalities that have absolute value signs around the variable. Example: |y – 5| ≤ 2 So the solutions to |y – 5| ≤ 2 are all numbers that have an absolute value less than or equal to 2, which means all numbers between -2 and 2 inclusive. -2 ≤ y – 5 ≤ 2 3≤y≤ 7 The solution to an absolute value inequality with a < or ≤ symbol forms a conjunction.

Solving Absolute Value Inequalities Solve and graph the solution of |2 c – 5| < 9 So the solutions are all numbers that have an absolute value less than 9 |2 c – 5| < 9 -9 < 2 c – 5 < 9 -4 < 2 c < 14 -2 < c < 7 Solve and graph the solution of: |3 t – 2| – 6 ≤ 1 |3 t – 2| ≤ 7 -7 ≤ 3 t – 2 ≤ 7 -5 ≤ 3 t ≤ 9 -5 ≤ t ≤ 3 3

Writing Absolute Value Inequalities The average number of cucumber seeds in a package is 25. The number of seeds in the package can vary by at most three. Write and solve an absolute value inequality to find the range of acceptable numbers of seeds in each package. |x – 25| ≤ 3 -3 ≤ x – 25 ≤ 3 22 ≤ x ≤ 28

Writing Absolute Value Inequalities The ideal circumference of a women’s basketball is 28. 75 in. The actual circumference may vary from the ideal by at most 0. 25 in. What are the acceptable circumferences for a women’s basketball? |x – 28. 75| ≤ 0. 25 -0. 25 ≤ x – 28. 75 ≤ 0. 25 28. 5 ≤ x ≤ 29