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Multi-Step Solving
Compound Inequalities
Absolute Value Inequalities
100
True/False: 0 is a solution to 2y + 1 < -3
What is false (2*0 + 1 = 1 and 1 > -3)
100

Solve: 5 ≤ v - 4 - 7

What is 16 ≤ v ?

100
Solve: 2y - 5 > 9 + 3y
What is y < -14 (or -14 > y)
100
Write the inequality for: "A number m is no less than –1 or less than or equal to -5 1/3"
What is: m ≥ -1 or m ≤ -5 1/3 ? The word "OR" must be present in answer.
100
Solution of: |y - 4| < 8
What is -4 < y < 12 ?
200
True/False: 9/2 is a solution to 5(2g - 7) ≥ 10
What is true ... 5(2*9/2 - 7) = 5(9 - 7) = 5(2) = 10... and 10 ≥ 10
200
Solve: -3(2n + 1) > 9
What is n < -2
200
Solve: 3(2 + r) ≥ 15 - 2r
What is r ≥ 9/5
200
The solution to: h + 7 < 5 or -9h < -45
What is: h < -2 or h > 5 ? The word "OR" must be present in answer.
200
Solution to: |3c + 4| > 7
What is c > 1 or c < -11/3 ?
300
Write the inequality to match the statement: "The difference between 9 and 4 times a number is at least 45."
What is 9 - 4x (>/-) 45?
300
Solve: -3n/5 ≥ -9
What is n ≤ 15
300
Solve: n/2 - 1/8 ≥ 3/4 + 5n/6. HINT: Cancel denominators first!!
What is n ≤ -21/8
300
Solution to: -6 < 1/3(6y + 12) < 14. For a compound inequality, final solution must also be combined.
What is: -5 < y < 5 ?
300
Solution of: |6b + 4| < -8
What is "No solution" ?
400

Write the inequality for the statement: "5 less than 6 times the quantity of 5f + 3 is no more than 5 times the sum of f and 12

What is 6(5f + 3) - 5 (</-) 5(f + 12)

400
Solution to: 4 < -2(y + 3)
What is y < -5 ?
400
17 - (4k - 2) ≥ 2(k + 3)
What is k ≤ 13/6
400
A tuxedo rental shop rents tuxedos with sleeve lengths from 20 inches to 40 inches. The shop says the length of the sleeves should be about 1.2 times a person's arm length. Write and solve a compound inequality that represents the arm lengths of people the shop does not provide tuxedos for.
20 > 1.2x OR 1.2X > 40 - MUST BE SHOWN x < 16 2/3 or x > 33 1/3 - The word "OR" must be present in answer.
400
Solution to: 3|3a + 8| - 11 < -5
What is -10/3 < a < -2 ?
500

Write an inequality for: "The rules for a book report say that the report should have 300 words with an absolute deviation of at most 20 words."

What is |x - 300|<20

500
Solve: 2/3 - 5n/3 ≤ -8/3
n ≥ 2
500
You must maintain a minimum balance of $50 in your checking account. You currently have a balance of $280. Write and solve an inequality that represents how many $20 bills you can withdraw from the account without going below the minimum balance. Your final answer should represent a realistic answer to this word problem.
280 - 20x ≥ 50 - MUST BE SHOWN x ≤ 11.5 (11 $20 bills)
500
4x - 9 < 9x + 6 < 4x + 16. Final answer of a compound inequality must have joined solution.
What is -3 < x < 2 ?
500
A nail manufacturer throws out nails with lengths that are not within 0.05 inch of the mean length of the batch. The lengths (in inches) of the nails in a batch are 0.42, 0.53, 0.55, 0.48, and 0.51. Which nail(s) should be thrown out? Write an absolute value inequality to model the situation, then give your answer.
What is .44, .55?