Algebraic Inequalities and Absolute Value Equations Quiz

Test your understanding of algebraic inequalities and absolute value equations with this quiz covering various scenarios and problem-solving techniques.

Practice Learn Test

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

x < 5

x > 5

x < 15

x > 15

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

x = 5

x = -2

x = 5/2

x = 10/3

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

x ≤ 3

x ≥ 3

x ≤ 6

x ≥ 6

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

x < -1 or x > 2

x < 0 or x > 4

x < -3 or x > 1

x < -2 or x > 3

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

x ≥ 3

x ≤ 3

x ≥ 4

x ≤ 4

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

x = -1 or x = 13/3

x = 13/3 or x = 5/3

x = 1 or x = 13/3

x = 13/3 or x = 3/5

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

-3 ≤ x < 7

-3 < x < 7

-3 ≤ x ≤ 7

-3 < x ≤ 7

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?

6 < x < 10

4 < x < 6

0 < x < 6

0 < x < 4

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

x < -4 and x > 7

x < -4 or x > 7

x < -4 or x < 7

x > -4 or x < 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?

5 < x < 15

5 < x < 10

10 < x < 15

0 < x < 5

#11

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

x ≤ -2 and x > 5

x ≤ -2 or x > 5

x ≤ -2 or x ≤ 5

x > -2 or x > 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?

7 < x < 12

7 < x < 17

12 < x < 17

0 < x < 7

#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

|x - 8| ≤ 7

|x - 5| ≥ 12

|x - 5| ≤ 12

#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

|x - 75| < 2

|x - 2| = 75

|x - 2| < 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

|x - 20| ≤ 40

|x - 40| ≥ 20

|x - 40| ≤ 20

#16

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

|x - 10| ≥ 50

|x - 50| ≤ 10

|x - 50| ≥ 10

|x - 10| ≤ 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

|x - 60| < 5

|x - 5| = 60

|x - 5| < 60