BELL-WORK New Study Island due Tuesday!

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Presentation transcript:

BELL-WORK New Study Island due Tuesday! Solve the inequalities, then graph the solution. 12x – 3x + 11 ≥ 4x – (17 – 9x) -8 ≤ 2x – 4 ≤ 4

Materials Check

Quiz 2.1 Quiz is tomorrow!

Exam 1.2 Review

HW 2.1 HW with corrections due Friday! Practice problems from today’s lesson are on the website!

HW 2.1(d) Solutions 1. x < -3 OR x ≥ 5; GRAPH 9. d < -4 OR d ≥ 2; GRAPH 3 10. c > 7 OR c < -5; GRAPH 12. z < 1; GRAPH 24. x < -4 OR x ≥ 2 27. r < 1 OR r > 10 29. y ≤ 18 OR y ≥ 61

Guiding question: What do absolute value inequalities convert to?

Inequalities Recap * Inequalities *Compound inequalities: Conjunction Disjunction

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 |2c – 5| < 9 So the solutions are all numbers that have an absolute value less than 9 |2c – 5| < 9 -9 < 2c – 5 < 9 -4 < 2c < 14 -2 < c < 7 Note: We write the conjunction only when the bars have been isolated. Solve and graph the solution of: |h – 3| < 5 |3t – 2| – 6 ≤ 1

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. 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?

Solving Absolute Value Inequalities Solve |v – 3| ≥ 4 So the solutions to |v – 3| ≥ 4 are all numbers that have an absolute value greater than or equal to 4, which means all numbers that are greater than or equal to 4 or less than or equal to -4. v – 3 ≥ 4 OR v – 3 ≤ -4 v ≥ 7 OR v ≤ -1 The solution to an absolute value inequality with a > or ≥ symbol forms a disjunction.

Solving Absolute Value Inequalities Solve and graph the solutions of: |x + 2 | ≥ 1 |2x + 4| > 5 3 + 4|2y – 3| > 11

Who wants to answer the Guiding question? What do absolute value inequalities convert to?