Algebraic Reasoning: Master Equations and Inequalities

Question 1

Two consecutive odd numbers add up to 36. Write an equation that represents this situation.

Accepted Answer

x + (x + 2) = 36

Answer

x - (x + 2) = 36

Answer

(x + 2) - x = 36

Question 2

Solve the inequality: 2x - 5 is greater than 9 and x - 2 is less than 10.

Accepted Answer

x is greater than 7 and less than 12

Answer

x is less than 2

Answer

x is greater than 7

Question 3

In the equation 3x + 5 = 16, what does the variable x represent?

Accepted Answer

The unknown value that solves the equation

Answer

The total of the numbers on the left side of the equation

Answer

The number multiplied by 3

Answer

The number added to 5

Question 4

Simplify the expression: 3(2x - 5) + 4x

Accepted Answer

6x - 15

Answer

2x - 15

Answer

6x + 15

Answer

10x - 15

Question 5

A fruit store sells apples and oranges. The store sold 150 fruits in total. The number of apples sold is double the number of oranges sold. Write a system of equations to represent this situation.

Accepted Answer

Let x be the number of apples and y be the number of oranges. The system of equations is:
    x + y = 150
    x = 2y

Answer

Let x be the number of apples and y be the number of oranges. The system of equations is:
    x - y = 150
    x = 2y

Answer

Let x be the number of apples and y be the number of oranges. The system of equations is:
    x + y = 150
    y = 2x

Answer

Let x be the number of apples and y be the number of oranges. The system of equations is:
    x - y = 150
    y = 2x

Question 6

A farmer has 250 feet of fencing to enclose a rectangular plot of land. If the length of the plot is 100 feet, what is the maximum possible width of the plot?

Accepted Answer

50 feet

Answer

100 feet

Answer

125 feet

Answer

250 feet

Question 7

Solve the inequality: 2x - 5 is greater than 7

Accepted Answer

x is greater than 6

Answer

x is less than 6

Answer

x is greater than 1

Answer

x is less than 1

Question 8

To solve the equation **2/3x + 1/6 = 5/6**, what should you do first?

Accepted Answer

Multiply both sides by 6 to clear the fractions.

Answer

Subtract 1/6 from both sides to isolate the variable.

Answer

Divide both sides by 2/3 to simplify the equation.

Answer

Add 1/3 to both sides to isolate the constant.

Question 9

Find the solution set for the inequality: x + 2 > 5

Accepted Answer

x > 3

Answer

x < 3

Answer

x > -3

Answer

x < -3

Question 10

Solve the equation: 2(y - 3) = 10

Accepted Answer

y = 7

Answer

y = 8

Answer

y = 9

Answer

y = 10

Question 11

Which property allows you to add the same number to both sides of an equation without changing its solution?

Accepted Answer

Additive Inverse Property

Answer

Associative Property

Answer

Distributive Property

Answer

Identity Property

Question 12

Find the degree of the polynomial 2x^3 - 4x + 5

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 13

Which of the following is an inequality?

Accepted Answer

x > 5

Answer

2x = 10

Answer

x + y = 7

Answer

3x - 5 = 0

Question 14

Which expression is equivalent to 2(x + 3)?

Accepted Answer

2x + 6

Answer

x + 6

Answer

2x + 3

Answer

4x + 3

Question 15

Evaluate the expression: 3x - 2y for x = 4 and y = -1

Accepted Answer

1

Answer

9

Answer

-1

Answer

-9

Question 16

What is the slope of the line y = 2x + 5?

Accepted Answer

2

Answer

5

Answer

7

Answer

-2

Question 17

What is the y-intercept of the line y = 2x + 5?

Accepted Answer

5

Answer

2

Answer

7

Answer

-2

Question 18

Find the inequality that represents the solution set of x is less than 5.

Accepted Answer

x < 5

Answer

x > 5

Answer

x ≥ 5

Answer

x ≤ 5

Question 19

A farmer has 240 feet of fencing to enclose a rectangular plot of land. If the length of the plot is 30 feet more than its width, what are the dimensions of the plot?

Accepted Answer

Width: 70 ft, Length: 100 ft

Answer

Width: 60 ft, Length: 90 ft

Answer

Width: 80 ft, Length: 110 ft

Answer

Width: 90 ft, Length: 120 ft

Question 20

Which of the following is NOT an algebraic expression?

Accepted Answer

3

Answer

5x

Answer

x + 3

Answer

x^2

Question 21

Which property justifies the equation: 5 + (x + 2) = (5 + x) + 2?

Accepted Answer

Associative Property of Addition

Answer

Commutative Property of Addition

Answer

Distributive Property

Answer

Identity Property of Addition

Question 22

Which of the following is equivalent to the expression (x + 2)(x - 3)?

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 23

Solve the one-step equation: 3y - 7 = 12

Accepted Answer

y = 9

Answer

y = 3

Answer

y = 6

Answer

y = 12

Question 24

Simplify the algebraic expression: 3xy + 2x

Accepted Answer

x(3y + 2)

Answer

5xy

Answer

2(x + 3y)

Answer

3(x + 2y)

Question 25

Simplify the algebraic expression: 3(2x - 4) - 2(x + 5)

Accepted Answer

6x - 14

Answer

4x - 22

Answer

6x + 14

Answer

4x + 22

Question 26

Which inequality represents the solution set of {x | x > 5}?

Accepted Answer

x > 5

Answer

x < 5

Answer

{x | x < 5}

Answer

{x | x ≥ 5}

Question 27

Find the area of the rectangle with length x and width y.

Accepted Answer

xy

Answer

x + y

Answer

x - y

Answer

x/y

Question 28

Solve for x in the equation: x + 5 = 12.

Accepted Answer

x = 7

Answer

x = 17

Answer

x = 5

Answer

x = 12

Question 29

Solve for x in the equation: 3(x + 2) = 15.

Accepted Answer

x = 5

Answer

x = 3

Answer

x = 7

Answer

x = 9

Question 30

Solve the inequality: 2x - 5 > 1.

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 1

Answer

x < 1

Question 31

Which of the following is a rational number?

Accepted Answer

0.12345

Answer

sqrt(2)

Answer

pi

Answer

e

Question 32

If x = 2, what is the value of y in the equation y + 3x = 12?

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Question 33

Simplify the expression: 2x(x - 3)

Accepted Answer

2x^2 - 6x

Answer

2x^2 - 3x

Answer

4x^2 - 3x

Answer

4x^2 - 6x

Question 34

Which expression is equivalent to (x + 2)^2?

Accepted Answer

x^2 + 2x + 4

Answer

x^2 - 4x + 4

Answer

x^2 + 4x + 4

Answer

x^2 - 4

Question 35

Which expression is equivalent to 5x + 3?

Accepted Answer

5(x + 3)

Answer

3(x + 5)

Answer

(5 + 3)x

Answer

x(5 + 3)

Question 36

Which inequality represents 'The number y is greater than or equal to -3'?

Accepted Answer

y ≥ -3

Answer

y > -3

Answer

y ≤ -3

Answer

y < -3

Question 37

Which of the following expressions is a polynomial?

Accepted Answer

x^2 + 2x - 1

Answer

x^2 + 2/x - 1

Answer

x^2 + √x - 1

Answer

x^2 + e^x - 1

Question 38

Solve for x: x - 7 = 12

Accepted Answer

19

Answer

5

Answer

-5

Answer

-19

Question 39

Which expression is equivalent to 2(x + 3)?

Accepted Answer

2x + 6

Answer

2x + 3

Answer

x + 6

Answer

6x

Question 40

Solve the inequality: x + 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Answer

x > -5

Answer

x < -5

Question 41

Simplify the expression: (2x - 3)(x + 2)

Accepted Answer

2x^2 - 3x + 4

Answer

2x^2 + 3x - 4

Answer

x^2 - 3x + 4

Answer

x^2 + 3x - 4

Question 42

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 43

Solve the equation: |x - 2| = 4

Accepted Answer

x = 6 or x = -2

Answer

x = 4 or x = -4

Answer

x = 2 or x = -2

Answer

x = 4 or x = -2

Question 44

Which of the following is an example of a rational number?

Accepted Answer

1/2

Answer

π

Answer

√2

Answer

e

Question 45

Which inequality symbol represents 'x is greater than or equal to 3'?

Accepted Answer

x ≥ 3

Answer

x ≤ 3

Answer

x > 3

Answer

x < 3

Question 46

Which of the following is NOT a property of equations?

Accepted Answer

Distributive Property

Answer

Reflexive Property

Answer

Transitive Property

Answer

Symmetric Property

Question 47

The perimeter of a rectangle is 24 cm. If its length is 3 cm more than its width, what are the dimensions of the rectangle?

Accepted Answer

(7 cm, 5 cm)

Answer

(6 cm, 6 cm)

Answer

(8 cm, 4 cm)

Answer

(9 cm, 3 cm)

Question 48

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x + 1)(x - 9)

Answer

(x - 3)(x - 3)

Question 49

Solve the equation: |x - 2| = 5

Accepted Answer

x = -3 or x = 7

Answer

x = 3 or x = 7

Answer

x = -3

Answer

x = 7

Question 50

Find the slope of the line that passes through the points (3, 5) and (7, 9)

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 51

Write the equation of the line that has a slope of -2 and passes through the point (1, 3)

Accepted Answer

y = -2x + 1

Answer

y = -2x + 5

Answer

y = 2x + 5

Answer

y = 2x + 1

Question 52

Find the value of x that makes the equation true: x + 5 = 10

Accepted Answer

x = 5

Answer

x = 15

Answer

x = -5

Answer

x = 10

Question 53

Simplify the expression: 2(x - 3) + 5

Accepted Answer

2x + 11

Answer

2x - 2

Answer

x - 1

Answer

x + 11

Question 54

Which inequality shows that the number y is at least -5?

Accepted Answer

y ≥ -5

Answer

y ≤ -5

Answer

y > -5

Answer

y < -5

Question 55

Simplify the expression: 3x(2x - 1)

Accepted Answer

6x² - 3x

Answer

5x - 3

Answer

6x³ - 3x²

Answer

6x² + 3x

Question 56

The perimeter of a rectangular garden is 24 cm. If the length of the garden is 6 cm, what is its width?

Accepted Answer

4 cm

Answer

6 cm

Answer

8 cm

Answer

12 cm

Question 57

Solve the equation: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = 10

Answer

x = 7

Answer

x = 9

Question 58

Which inequality represents the statement: The number of books on a shelf is less than 20.

Accepted Answer

x < 20

Answer

x ≤ 20

Answer

x > 20

Answer

x ≥ 20

Question 59

Solve the system of equations: x + y = 7, x - y = 1

Accepted Answer

x = 4, y = 3

Answer

x = 1, y = 0

Answer

x = 2, y = 1

Answer

x = 3, y = 2

Question 60

Find the slope of the line passing through the points (1, 3) and (3, 9)

Accepted Answer

3

Answer

2

Answer

1

Answer

4

Question 61

Write the equation of the line with a slope of -2 and a y-intercept of 1

Accepted Answer

y = -2x + 1

Answer

y = -2x - 1

Answer

y = 2x + 1

Question 62

Solve for x: 2x - 5 < 11

Accepted Answer

x < 8

Answer

x > 6

Answer

x < 6

Answer

x > 8

Question 63

Which of the following expressions is equivalent to 3(x + 2)?

Accepted Answer

3x + 6

Answer

3x - 6

Answer

x - 6

Answer

x + 6

Question 64

Simplify the expression: 2x^2 + 3x - 5x - 6

Accepted Answer

2x^2 - 2x - 6

Answer

x^2 - 2x - 6

Answer

2x^2 + 8x - 6

Answer

x^2 + 3x - 6