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.

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

x < 5

x > 5

x < 15

x > 15

1 answered

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

x = 5

x = -2

x = 5/2

x = 10/3

1 answered

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

x ≤ 3

x ≥ 3

x ≤ 6

x ≥ 6

1 answered

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

1 answered

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

x ≥ 3

x ≤ 3

x ≥ 4

x ≤ 4

1 answered

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

1 answered

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

1 answered

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

2 answered

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

1 answered

#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

2 answered

#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

2 answered

#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

1 answered

#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

1 answered

#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

1 answered

#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

1 answered

#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

3 answered

#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

1 answered

Algebraic Inequalities and Absolute Value Equations Quiz

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

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

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

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

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

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

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

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

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?

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

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?

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?

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

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

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

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

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