Answers 4413VA ALGEBRA 3 SEM ASolving Compound Inequalities

Solving Compound Inequalities Answers

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Solve for x.0 ≤ 3x – 6 ≤ 18

0 ≤ x ≤ 8

2 ≤ x ≤ 8

x ≤ 0 or x ≥ 8

x ≤ 2 or x ≥ 8

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Phyllis solved the compound inequality 16 ≤ 2(3x – 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x.Which graph represents her solution?

A number line with a point at 3 with a bold line pointing to the right stopping at the open circle at 5.

A number line with an open circle at 3 with a bold line pointing to the right stopping at the point 5.

A number line with a point at 3 with a bold line pointing to the left and an open circle at 5 with a bold line pointing to the right.

A number line with an open circle at 3 with a bold line pointing to the left and a point at 5 with a bold line pointing to the right.

Mrs. Sawyer estimates that a quiz will take students no fewer than 11 minutes but no more than 41 minutes to complete. She allots 1 minute for passing out the papers and instructions and then students will complete a 20-question quiz. Which compound inequality represents x, the average amount of time a student spends on each question?

1 + 20x > 11 or 1 + 20x < 41

11 < 1 + 20x < 41

11 ≤ 1 + 20x ≤ 41

1 + 20x ≥ 11 or 1 + 20x ≤ 41

For a wrestler to qualify in his weight class, he needs to weigh more than 165 pounds but less than or equal to 185 pounds. He currenty weighs 189 pounds and is losing 0.5 of a pound per week.

165 ≤ 189 – 0.5w < 185

165 < 189 – 0.5w ≤ 185

165 > 189 – 0.5w or 185 ≤ 189 – 0.5w

165 ≥ 189 – 0.5w or 185 < 189 – 0.5w

Solve for x.5x – 10 > 20 or 5x – 10 ≤ –15

–5 ≤ x < 6

–1 ≤ x < 6

x ≤ –5 or x > 6

x ≤ –1 or x > 6

Ava solved the compound inequality + 7 < –1 or 2x – 1 ≥ 9 for all possible values of x. Which graph represents the solution set?

A number line with a point at negative 32 with a bold line pointing to the left and an open circle at 5 with a bold line pointing to the right.

A number line with an open circle at negative 32 with a bold line pointing to the left and a point at 5 with a bold line pointing to the right.

A number line with a point at negative 32 with a bold line pointing to the right stopping at the open circle at 5.

A number line with an open circle at negative 32 with a bold line pointing to the right stopping at the point 5.

Which is the best interpretation of the solution set for the compound inequality?3(2x + 1) > 21 or 4x + 3 < 3x + 7

no solution

3 < x < 4

x 4

all real numbers

A sugar solution currently measures 250 degrees Fahrenheit. The temperature of the solution increases 5 degrees per minute. The sugar solution will caramelize at temperatures greater than 310 and less than 338 degrees Fahrenheit. Which inequality can be used to find x, the number of minutes it will take for the solution to begin caramelizing?

310 < 250 + 5x < 338

310 < 5(x + 250) < 338

Which compound inequality has no solution?

x > 2 and 3x ≤ 9

x > 1 and 2x ≤ –2

x > –1 and 4x ≥ –8

x > –2 and 5x ≥ 15

Which best describes the solution set for the inequality below?3x + 7 ≤ 4x – 8 or –2x + 3 ≥ 1

x ≤ 1 or x ≥ 15

x ≥ 1 or x ≤ 15

x ≥ 1

x ≤ 15

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Solving Compound Inequalities Answers

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