Expressions and Equations: Master Algebra for Seventh Graders

Question 1

Which inequality describes the points that lie below the line y = 2x - 1?

Accepted Answer

y < 2x - 1

Answer

y > 2x - 1

Answer

y ≥ 2x - 1

Answer

y ≤ 2x - 1

Question 2

Simplify the expression: 3x + 2y - 5

Accepted Answer

(3x + 2y) - 5

Answer

(3x - 5) + 2y

Answer

3(x + 2y) - 5

Answer

3x + 2(y - 5)

Question 3

Translate the following statement into an inequality: The sum of a number and 4 is greater than 10:

Accepted Answer

x + 4 > 10

Answer

x - 4 > 10

Answer

x - 4 < 10

Answer

x + 4 < 10

Question 4

Write an expression for the area of a rectangle with a length of (x + 3) and a width of (2x - 1):

Accepted Answer

2x^2 + 5x - 3

Answer

x^2 - x - 3

Answer

2x^2 - x - 3

Answer

x^2 + 5x - 3

Question 5

Simplify the fraction: (x^2 - 4) / (x - 2):

Accepted Answer

(x + 2)

Answer

(x - 2)

Answer

(x^2 - 2)

Answer

(x^2 + 2)

Question 6

Which of the following inequalities represents the statement 'x is greater than or equal to 3'?

Accepted Answer

$x ≥ 3$

Answer

$x ≤ 3$

Answer

$x < 3$

Answer

$x > 3$

Question 7

Which of the following is the graph of the equation y equals 2x minus 1?

Accepted Answer

A line with a slope of 2 and a y-intercept of -1

Answer

A line with a slope of -2 and a y-intercept of 1

Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A line with a slope of -2 and a y-intercept of -1

Question 8

Find the solution to the inequality: 2x - 5 is less than 11.

Accepted Answer

x is less than 8

Answer

x is greater than 8

Answer

x is less than 6

Answer

x is greater than 6

Question 9

Find the value of x in the equation: 2x + 5 equals 13

Accepted Answer

x equals 4

Answer

x equals 5

Answer

x equals 6

Answer

x equals 7

Question 10

Solve the linear inequality and graph its solution set: 2x - 5 < 9

Accepted Answer

x < 7

Answer

x > 7

Answer

x < 2

Answer

x ≥ 7

Question 11

Find the value of x in the equation: 2x + 5 equals 13

Accepted Answer

x equals 4

Answer

x equals 8

Answer

x equals 6

Answer

x equals 2

Question 12

Simplify the expression: 2x + 3y - 5

Accepted Answer

2x + 3y - 5

Answer

x + 3y - 2

Answer

2(x + 3y - 5)

Answer

5 - 3y - 2x

Question 13

Find the value of x in the equation: 2x + 5 equals 13

Accepted Answer

x equals 4

Answer

x equals 6

Answer

x equals 8

Question 14

Find the value of x in the equation: 2x + 5 equals 13

Accepted Answer

x equals 4

Answer

x equals 6

Answer

x equals 8

Answer

x equals 10

Question 15

Translate the verbal expression into an algebraic inequality: 'A number x multiplied by 5 is greater than 10'

Accepted Answer

x * 5 > 10

Answer

x + 5 > 10

Answer

x * 5 < 10

Question 16

Which is NOT a property of real numbers?

Accepted Answer

Inverse property of subtraction

Answer

Commutative property of addition

Answer

Associative property of multiplication

Answer

Distributive property of multiplication over addition

Question 17

What are the solutions to the system of equations: x + y = 5, x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = -3, y = -2

Answer

x = 2, y = 3

Answer

x = -2, y = -3

Question 18

Which of the following is an example of an algebraic expression?

Accepted Answer

x + 5

Answer

5

Answer

x

Answer

5 = x

Question 19

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

Accepted Answer

2x + 11

Answer

x + 11

Answer

2x + 5

Answer

x + 5

Question 20

Solve the equation: x - 5 = 10

Accepted Answer

x = 15

Answer

x = 5

Answer

x = 10

Answer

x = -5

Question 21

Translate the statement into an algebraic inequality: A number x is greater than or equal to 5

Accepted Answer

x ≥ 5

Answer

x > 5

Answer

x ≤ 5

Question 22

Which of the following is an algebraic expression?

Accepted Answer

2x + 5

Answer

x = 5

Answer

5 < x

Question 23

Solve the equation: x + 5 = 10

Accepted Answer

5

Answer

15

Answer

20

Question 24

Solve the inequality: x - 2 > 5

Accepted Answer

x > 7

Answer

x < 7

Answer

x > 5

Question 25

Which of the following is a system of equations?

Accepted Answer

x + y = 5, x - y = 1

Answer

5 < x

Answer

x = 5

Question 26

Solve the system of equations: x + y = 5, x - y = 1

Accepted Answer

x = 3, y = 2

Answer

x = 5, y = 0

Answer

x = 1, y = 4

Question 27

Factor the expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 2)(x + 2)

Answer

(x - 2)(x - 2)

Question 28

Simplify the expression: (x + 2)^2

Accepted Answer

x^2 + 4x + 4

Answer

x^2 + 2x + 4

Answer

x^2 - 4x + 4

Question 29

Translate the phrase '17 less than twice a number' into an algebraic equation.

Accepted Answer

2x - 17 = 0

Answer

17x - 2 = 0

Answer

2x + 17 = 0

Answer

17 - 2x = 0

Question 30

Which inequality represents the statement 'x is no less than 10'?

Accepted Answer

x ≥ 10

Answer

x < 10

Answer

x ≤ 10

Answer

x > 10

Question 31

The length of a rectangle is 5 cm more than twice its width. If the width is represented by 'w', what is the algebraic expression for the length?

Accepted Answer

2w + 5

Answer

w + 5

Answer

2w - 5

Question 32

Evaluate the expression 4x - 3 when x = 5

Accepted Answer

17

Answer

12

Answer

21

Answer

8

Question 33

Which inequality is represented by the graph below? (Assume a number line with a closed circle at -2 and shading to the left)

Accepted Answer

x ≤ -2

Answer

x ≥ -2

Answer

x > -2

Answer

x < -2

Question 34

The perimeter of a rectangular garden is 24 cm. If the length of the garden is 3 cm more than its width, what is the width of the garden?

Accepted Answer

4.5 cm

Answer

6 cm

Answer

7.5 cm

Answer

3 cm

Question 35

Which expression represents the sum of 5 and the product of a number and 3?

Accepted Answer

5 + 3x

Answer

5x + 15

Answer

5 + x + 3

Answer

5x + 3

Question 36

Which of the following expressions represents "five more than twice a number n"?

Accepted Answer

2n + 5

Answer

2(n - 5)

Answer

5 - 2n

Question 37

If x = 4, what is the value of the expression 3x + 5?

Accepted Answer

17

Answer

11

Answer

15

Answer

22

Question 38

Simplify the expression: 6y + 2y - 5y

Accepted Answer

3y

Answer

12y

Answer

11y

Answer

y

Question 39

Solve for x: 3x - 7 = 10

Accepted Answer

6

Answer

4

Answer

3

Question 40

Solve for y: y - 6 < 9

Accepted Answer

y < 15

Answer

y ≤ 15

Answer

y ≥ 15

Answer

y > 15

Question 41

If 3 apples cost $6, which equation can be used to find the cost (c) of one apple?

Accepted Answer

3c = 6

Answer

6 - c = 3

Answer

c/3 = 6

Answer

3 + c = 6

Question 42

The sum of two consecutive integers is 25. What is the smaller integer?

Accepted Answer

12

Answer

14

Answer

11

Answer

13

Question 43

Which expression is equivalent to 3(x + 2) + 5?

Accepted Answer

3x + 11

Answer

15x + 10

Answer

6x + 10

Answer

x + 11

Question 44

Solve for x: 2x - 5 = 11

Accepted Answer

8

Answer

10

Answer

6

Question 45

Which inequality represents the solution set of x + 3 > 7?

Accepted Answer

x > 4

Answer

x < -4

Answer

x < 4

Answer

x > -4

Question 46

A farmer has 120 feet of fencing to enclose a rectangular garden. If the length of the garden is 5 feet more than its width, what are the dimensions of the garden?

Accepted Answer

25 ft x 50 ft

Answer

15 ft x 30 ft

Answer

30 ft x 40 ft

Answer

20 ft x 60 ft

Question 47

Which system of equations represents the lines that intersect at the point (2, 3)?

Accepted Answer

y = x + 1 and y = -x + 5

Answer

y = 2x + 1 and y = -x + 3

Answer

y = x + 3 and y = -2x + 5

Answer

y = 2x - 1 and y = x + 5

Question 48

Which expression represents the perimeter of a rectangle with a length of (x + 3) cm and a width of (x - 2) cm?

Accepted Answer

4x + 1

Answer

4x - 1

Answer

2x - 5

Answer

2x + 1

Question 49

Solve for y: 2y + 4 = 12

Accepted Answer

4

Answer

2

Answer

8

Answer

6

Question 50

Which inequality represents the solution set of -2(x - 1) > 6?

Accepted Answer

x < -2

Answer

x > 2

Answer

x < 2

Answer

x > -2

Question 51

A store sells apples for $0.50 each and oranges for $0.75 each. If a customer buys x apples and y oranges, which expression represents the total cost of the fruit?

Accepted Answer

0.50x + 0.75y

Answer

x + y

Answer

x * y

Answer

0.50x - 0.75y

Question 52

Which equation represents the line that passes through the points (1, 3) and (-1, 1)?

Accepted Answer

y = x + 2

Answer

y = 2x + 1

Answer

y = x - 2

Question 53

Which of the following is an example of an algebraic expression?

Accepted Answer

2x + 5

Answer

5 > 2

Answer

x = 5

Answer

5 + 5

Question 54

Solve for x: x + 5 = 12

Accepted Answer

7

Answer

5

Answer

17

Answer

12

Question 55

Which of the following is an inequality?

Accepted Answer

x > 5

Answer

2x + 5 = 12

Answer

5 + 5

Answer

x = 5

Question 56

Solve the inequality: x - 2 < 5

Accepted Answer

x < 7

Answer

x = 7

Answer

x < 5

Answer

x > 7

Question 57

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

Accepted Answer

2x + 1

Answer

x + 1

Answer

x - 1

Answer

2x - 1

Question 58

Which of the following is the solution to the system of equations: x + y = 5 and x - y = 1?

Accepted Answer

(3, 2)

Answer

(4, 1)

Answer

(2, 3)

Answer

(1, 4)

Question 59

Solve for y: 2x - 3y = 6

Accepted Answer

y = (2/3)x - 2

Answer

y = (3/2)x - 2

Answer

y = (3/2)x + 2

Answer

y = (2/3)x + 2

Question 60

Which of the following is an example of a quadratic equation?

Accepted Answer

x^2 + 5x + 6 = 0

Answer

5x + 6 = 0

Answer

x - 5 = 0

Question 61

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 62

Solve the quadratic equation: x^2 - 5x + 6 = 0

Accepted Answer

x = 2 or x = 3

Answer

x = -1 or x = -6

Answer

x = -2 or x = -3

Answer

x = 1 or x = 6