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Algebraic Inequalities and Absolute Value Equations Quiz

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#1

Which of the following represents the solution set for the inequality 3x - 5 < 10?

x < 15
Explanation

Solution set indicates x is less than 15.

#2

What is the solution to the absolute value equation |2x - 3| = 7?

x = 5/2
Explanation

Absolute value of (2x - 3) equals 7 implies x equals 5/2.

#3

For which values of x is the inequality 2x + 3 ≤ 9 true?

x ≤ 3
Explanation

Values of x satisfying 2x + 3 being less than or equal to 9 are x being less than or equal to 3.

#4

What is the solution set for the absolute value inequality |5x - 2| > 8?

x < -2 or x > 3
Explanation

Values of x satisfying |5x - 2| being greater than 8 are x being less than -2 or greater than 3.

#5

What is the solution to the inequality 4x + 7 ≥ 19?

x ≥ 3
Explanation

Values of x satisfying 4x + 7 being greater than or equal to 19 are x being greater than or equal to 3.

#6

Find the solution set for the absolute value equation |3x - 5| = 8.

x = 13/3 or x = 5/3
Explanation

Absolute value of (3x - 5) equals 8 implies x equals 13/3 or 5/3.

#7

Which of the following compound inequalities represents 'x is greater than or equal to -3 and less than 7'?

-3 ≤ x ≤ 7
Explanation

Compound inequality describes x being greater than or equal to -3 but less than 7.

#8

If the ratio of the lengths of two sides of a triangle is 3:4, and the length of the third side is 10, what is the range of possible values for the length of the shorter side?

4 < x < 6
Explanation

The shorter side's length lies between 4 and 6.

#9

Which of the following compound inequalities represents 'x is less than -4 or x is greater than 7'?

x < -4 or x > 7
Explanation

Compound inequality describes x being less than -4 or greater than 7.

#10

If the sum of the lengths of two sides of a triangle is 15 and the length of the third side is 10, what is the range of possible values for the length of the longer side?

10 < x < 15
Explanation

The longer side's length ranges between 10 and 15.

#11

Which of the following compound inequalities represents 'x is less than or equal to -2 or x is greater than 5'?

x ≤ -2 or x > 5
Explanation

Compound inequality describes x being less than or equal to -2 or greater than 5.

#12

If the ratio of the lengths of two sides of a triangle is 4:5, and the length of the third side is 12, what is the range of possible values for the length of the longer side?

12 < x < 17
Explanation

The longer side's length ranges between 12 and 17.

#13

A desk drawer must have a width that is at least 5 inches but no more than 12 inches. Which of the following absolute value inequalities represents this situation?

|x - 8| ≤ 7
Explanation

Absolute value of (x - 8) is less than or equal to 7, indicating x is within 7 units of 8.

#14

The temperature in a room must be maintained within 2 degrees of 75 degrees Fahrenheit. Which absolute value inequality represents this requirement?

|x - 75| < 2
Explanation

Absolute value of (x - 75) is less than 2, indicating x is within 2 units of 75.

#15

The price of a product must be discounted by at least 20% but no more than 40%. Which absolute value inequality represents this requirement?

|x - 20| ≤ 40
Explanation

Absolute value of (x - 20) is less than or equal to 40, indicating x is within 40 units of 20.

#16

The weight of a package must be within 10 ounces of 50 ounces. Which absolute value inequality represents this requirement?

|x - 50| ≤ 10
Explanation

Absolute value of (x - 50) is less than or equal to 10, indicating x is within 10 units of 50.

#17

The speed of a car must be within 5 miles per hour of 60 miles per hour. Which absolute value inequality represents this requirement?

|x - 60| < 5
Explanation

Absolute value of (x - 60) is less than 5, indicating x is within 5 units of 60.

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