Master Inequalities: Enhance Your Math Education Skills

Question 1

Which of the following is the definition of an inequality?

Accepted Answer

An expression that uses a greater than sign (>), less than sign (<), greater than or equal to sign (>=), or less than or equal to sign (<=)

Answer

An equation that uses an equal sign (=)

Answer

A mathematical statement that is always true

Answer

An expression that uses a variable

Question 2

Solve the inequality: 3x - 4 < 11

Accepted Answer

x < 5

Answer

x > 5

Answer

x < 2.33

Answer

x > 2.33

Question 3

Which of the following is the graph of the inequality x + y > 2?

Accepted Answer

A line with a solid boundary at y = -2

Answer

A line with a dashed boundary at y = -2

Answer

The entire x-axis

Answer

The entire y-axis

Question 4

Solve the inequality: |2x - 5| > 3

Accepted Answer

x < 1 or x > 4

Answer

x < -1 or x > 4

Answer

1 < x < 4

Answer

-1 < x < 4

Question 5

Which of the following is NOT a property of inequalities?

Accepted Answer

If a/b > 0, then a and b have the same sign

Answer

If a > b, then a + c > b + c for any real number c

Answer

If a > b and b > c, then a > c

Answer

If a > b, then -a < -b

Question 6

Which of the following is NOT a property of inequalities?

Accepted Answer

Distributivity

Answer

Transitivity

Answer

Reflexivity

Answer

Symmetry

Question 7

Which of the following is NOT a type of inequality?

Accepted Answer

Cubic inequality

Answer

Linear inequality

Answer

Quadratic inequality

Answer

Absolute value inequality

Question 8

Solve the absolute value inequality: |x - 2| < 1. What is the solution set?

Accepted Answer

1 < x < 3

Answer

x < 1 or x > 3

Answer

x < 3 or x > 1

Answer

3 < x < 1

Question 9

Which of the following accurately represents the inequality 'x is greater than or equal to 5'?

Accepted Answer

x ≥ 5

Answer

5 < x

Answer

x ≤ 5

Answer

5 > x

Question 10

Find the solution to the inequality: 3x - 5 < 10.

Accepted Answer

x < 5

Answer

x > 5

Answer

x ≤ 5

Answer

x ≥ 5

Question 11

Identify the type of inequality: 4 - 3x ≤ 2x + 5.

Accepted Answer

Linear inequality

Answer

Quadratic inequality

Answer

Absolute value inequality

Answer

Rational inequality

Question 12

Which property of inequalities is demonstrated in the statement '-5 < 0 and 0 < 5, therefore -5 < 5'?

Accepted Answer

Transitive property

Answer

Additive inverse property

Answer

Multiplication property

Answer

Division property

Question 13

Solve the compound inequality: -2 < x - 5 ≤ 3.

Accepted Answer

[-2, 8]

Answer

(3, 8]

Answer

[-2, 3]

Answer

(3, 8)

Question 14

Which of the following expressions represents an inequality?

Accepted Answer

x is greater than 5

Answer

x equals 5

Answer

x plus 5 equals 10

Answer

x divided by 5

Question 15

What property of inequalities states that if a is less than b and b is less than c, then a must be less than c?

Accepted Answer

Transitive property

Answer

Reflexive property

Answer

Antisymmetric property

Answer

Symmetric property

Question 16

Which of the following graphs represents the inequality y is less than 2x plus 1?

Accepted Answer

A line with a negative slope, below the line y equals 2x plus 1

Answer

A line with a positive slope, above the line y equals 2x plus 1

Answer

A line with a negative slope, above the line y equals 2x plus 1

Answer

A line with a positive slope, below the line y equals 2x plus 1

Question 17

Which of the following inequalities is equivalent to the absolute value of x minus 3 is less than 2?

Accepted Answer

Negative 2 is less than x minus 3 and x minus 3 is less than 2

Answer

Negative 2 is greater than x minus 3 and x minus 3 is greater than 2

Answer

2 is less than x minus 3 and x minus 3 is less than 4

Answer

2 is greater than x minus 3 and x minus 3 is greater than 4

Question 18

Which of the following is an example of a compound inequality?

Accepted Answer

x is greater than 5 and x is less than 10

Answer

x is less than 5

Answer

x plus 5 is greater than 10

Answer

x minus 5 is less than 10

Question 19

Which of the following inequalities represents the statement "the quantity of two numbers added together is greater than 10"?

Accepted Answer

x plus y is greater than 10

Answer

x plus y is less than 10

Answer

x minus y is greater than 10

Answer

x minus y is less than 10

Question 20

Define inequalities in your own words, highlighting their comparison function and the symbols used to represent them.

Accepted Answer

Inequalities compare the values of two expressions using symbols like <, >, ≤, and ≥.

Answer

Inequalities show the equality of two expressions using symbols like = and ≠.

Answer

Inequalities represent the difference between two expressions using symbols like +, -, *, and ÷.

Answer

Inequalities indicate the sum of two expressions using symbols like ∩ and ∪.

Question 21

Solve the inequality 3x - 7 < 14 and provide a step-by-step explanation of your solution.

Accepted Answer

x < 7

Answer

x > 7

Answer

x < -7

Answer

x > -7

Question 22

Which property of inequalities is illustrated in the statement: If a < b and b < c, then a < c?

Accepted Answer

Transitive property

Answer

Reflexive property

Answer

Symmetric property

Answer

Trichotomy property

Question 23

Solve the quadratic inequality x² - 4x + 3 < 0 and explain the method used to find its solution set.

Accepted Answer

x < 1 or x > 3

Answer

x < -1 or x > -3

Answer

x < 3 or x > 1

Answer

x < -3 or x > -1

Question 24

Define an inequality.

Accepted Answer

A mathematical statement comparing two expressions using symbols <, >, ≤, or ≥

Answer

An equation with no solution

Answer

An expression involving variables

Answer

A statement that is always true

Question 25

Solve the inequality: 3x - 2 > 13

Accepted Answer

x > 5

Answer

x < 5

Answer

x ≥ 5

Answer

x ≤ 5

Question 26

Translate the verbal inequality 'the sum of x and 3 is greater than or equal to 7' into an algebraic expression.

Accepted Answer

x + 3 ≥ 7

Answer

x + 3 > 7

Answer

x - 3 > 7

Answer

x - 3 ≥ 7

Question 27

Solve the inequality: 2x - 1 > 5.

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 2

Question 28

Which property of inequalities justifies the statement: if x < y and y < z, then x < z?

Accepted Answer

Transitive property

Answer

Reflexive property

Answer

Additive property

Answer

Symmetric property

Question 29

Which inequality represents the set of all numbers that are at least -5?

Accepted Answer

x ≥ -5

Answer

x ≤ -5

Answer

x < -5

Answer

x > -5

Question 30

What is the definition of an inequality?

Accepted Answer

A mathematical statement that compares two expressions using the symbols <, >, ≤, or ≥.

Answer

An equation with one or more variables.

Answer

A statement that is either true or false.

Question 31

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x < 11

Answer

x > 11

Answer

x < 8

Question 32

Which of the following inequalities is equivalent to x ≤ 5?

Accepted Answer

5 - x ≥ 0

Answer

5x ≤ 1

Answer

-x ≤ 5

Answer

x ≥ 5

Question 33

Graph the inequality: y < 2x + 1

Accepted Answer

A line with slope 2 and y-intercept 1, with the region below the line shaded.

Answer

A line with slope -2 and y-intercept 1, with the region above the line shaded.

Answer

A line with slope 1 and y-intercept 2, with the region below the line shaded.

Question 34

Solve the system of inequalities: y > x + 1 and y < 2x - 3

Accepted Answer

The region above the line y = x + 1 and below the line y = 2x - 3.

Answer

The region below the line y = x + 1 and above the line y = 2x - 3.

Answer

The region to the left of the line y = x + 1 and to the right of the line y = 2x - 3.

Question 35

What is an example of a quadratic inequality?

Accepted Answer

x^2 - 4 < 0

Answer

x + 2 > 5

Answer

y > 2x - 3

Answer

x ≥ 10

Question 36

What is a valid method for solving the inequality |x - 2| > 3?

Accepted Answer

Split into two cases: x - 2 > 3 and x - 2 < -3

Answer

Multiply both sides by -1

Answer

Take the square root of both sides

Answer

Subtract 2 from both sides

Question 37

Which inequality represents the set of all real numbers?

Accepted Answer

-∞ < x < ∞

Answer

x ≤ 1

Answer

0 ≤ x ≤ 1

Answer

x ≥ 0

Question 38

Which inequality represents the statement 'x is greater than or equal to 5'?

Accepted Answer

x ≥ 5

Answer

x ≤ 5

Answer

x < 5

Answer

x > 5

Question 39

Solve the absolute value inequality: |x + 2| > 4

Accepted Answer

x < -6 or x > 2

Answer

-6 < x < 2

Answer

x > -6

Answer

x < 2

Question 40

Which point lies within the solution region of the inequality y > 2x - 1?

Accepted Answer

(2, 3)

Answer

(1, 1)

Answer

(-1, 0)

Answer

(0, -1)

Question 41

When graphing the inequality y ≤ -x + 3, which boundary line type is appropriate?

Accepted Answer

Solid line

Answer

Dashed line

Answer

Horizontal line

Answer

Vertical line

Question 42

Graph the inequality: y > -2x + 3

Accepted Answer

A line with a slope of -2 and y-intercept of 3, with the shaded region above the line

Answer

A line with a slope of -2 and y-intercept of 3, with the shaded region below the line

Answer

An image of a line with slope -2 and y-intercept 3, with no shading

Answer

A line with a slope of 2 and y-intercept of 3, with the shaded region above the line

Question 43

What does the solution set of 2x - 3y > 6 represent?

Accepted Answer

The region above the line 2x - 3y = 6

Answer

The region on the line 2x - 3y = 6

Answer

The region below the line 2x - 3y = 6

Answer

The region below the line y = 2x - 6

Question 44

Which property can be used to perform addition or subtraction on both sides of an inequality without affecting its validity?

Accepted Answer

Transitive Property

Answer

Reflexive Property

Answer

Multiplication Property

Answer

Substitution Property

Question 45

Find the solution to the inequality: |x - 2| < 5

Accepted Answer

-7 < x < 12

Answer

-2 < x < 12

Answer

-5 < x < 10

Answer

-7 < x < 7

Question 46

Which inequality represents the set of all non-negative real numbers?

Accepted Answer

x ≥ 0

Answer

x < 0

Answer

x > 0

Answer

x ≤ 0

Question 47

Graph the inequality: y > -2x + 1

Accepted Answer

Image of a line with a dashed boundary above and to the right of the line.

Answer

Image of a line with a solid boundary above and to the right of the line.

Answer

Image of a line with a dashed boundary below and to the left of the line.

Answer

Image of a line with no boundary or shading.

Question 48

Which operation is NOT permissible when solving an inequality?

Accepted Answer

Dividing both sides by a negative number

Answer

Multiplying both sides by the same positive number

Answer

Subtracting the same number from both sides

Answer

Adding the same number to both sides

Question 49

Simplify the inequality: 2(x - 1) + 3x > 5

Accepted Answer

x > 2

Answer

x > 1

Answer

x < 1

Answer

x < 2

Question 50

Solve the compound inequality: -2 < x - 5 ≤ 3

Accepted Answer

0 ≤ x ≤ 8

Answer

-2 ≤ x ≤ 3

Answer

-2 < x < 8

Answer

0 < x < 8

Question 51

Which of the following inequalities is equivalent to x² - 4 < 0?

Accepted Answer

-2 < x < 2

Answer

x < -2 or x > 2

Answer

x² < 4

Answer

x > -2 and x < 2

Question 52

Determine the solution set of the inequality: |3x + 4| > 7

Accepted Answer

x < -3 or x > 1

Answer

x < -3 or x > -1

Answer

x > -3 and x < 1

Answer

x > 3 or x < -1

Question 53

Which inequality represents the solution set of the graph below? [Image of a shaded region below a horizontal line at y = 2]

Accepted Answer

y < 2

Answer

y > 2

Answer

y ≥ 2

Answer

y ≤ 2