Equations and Inequalities: Master the Basics of Algebra

Question 1

Solve for x: x + 5 = 12

Accepted Answer

7

Answer

5

Answer

17

Answer

22

Question 2

Solve for y: 3(y - 2) = 15

Accepted Answer

7

Answer

3

Answer

5

Answer

9

Question 3

Represent the statement 'x is less than or equal to 10' using mathematical notation:

Accepted Answer

x ≤ 10

Answer

x < 10

Answer

x > 10

Answer

x ≥ 10

Question 4

Find the value of x in the equation: 2x - 5 equals 11

Accepted Answer

x equals 8

Answer

x equals 6

Answer

x equals 10

Question 5

Which of the following is an equation?

Accepted Answer

x = 5

Answer

x > 10

Answer

x + 5

Answer

x < 2

Question 6

What is the solution to the inequality: x - 5 > 2?

Accepted Answer

x > 7

Answer

x < 7

Answer

x ≥ 7

Answer

x ≤ 7

Question 7

Which of the following is not a property of equality?

Accepted Answer

Distributive property

Answer

Reflexive property

Answer

Symmetric property

Answer

Transitive property

Question 8

Solve the equation: |x - 5| = 3

Accepted Answer

x = 2 or x = 8

Answer

x = 8

Answer

x = 2

Answer

x = -2 or x = 8

Question 9

A store sells apples for $0.50 each. If you buy x apples, how do you calculate the total cost?

Accepted Answer

0.50x

Answer

50x

Answer

x/0.50

Answer

50/x

Question 10

Solve for y in the inequality: 2y + 5 > 15

Accepted Answer

y > 5

Answer

y < 5

Answer

y > 10

Answer

y < 10

Question 11

Which of these statements is always true?

Accepted Answer

5 = 5

Answer

5 < 5

Answer

5 > 5

Answer

5 ≠ 5

Question 12

Which of these represents a variable?

Accepted Answer

x

Answer

5

Answer

=

Answer

7

Question 13

Which of these is an algebraic expression?

Accepted Answer

x + 5

Answer

x = 5

Answer

x < 5

Answer

x > 5

Question 14

Find the value of z in the equation: 3z + 4 = 19

Accepted Answer

z equals 7

Answer

z equals 3

Answer

z equals 5

Answer

z equals 9

Question 15

Which of the following statements shows an inequality?

Accepted Answer

y - 3 is greater than 7

Answer

x + 5 is equal to 10

Answer

2x equals 6

Answer

z is equal to 4 plus 2

Question 16

Which graph represents the inequality x + 2 is less than 5?

Accepted Answer

A line with a shaded area below it

Answer

A line with a shaded area above it

Answer

A line with no shaded area

Answer

A circle with a shaded area inside it

Question 17

Solve the equation: x + 5 = 12. What is the value of x?

Accepted Answer

7

Answer

5

Answer

9

Answer

17

Question 18

Solve the inequality: 2x - 1 > 5. What is the solution?

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 2

Answer

x < 2

Question 19

Which of the following is NOT a solution to the equation 3(x - 2) = 12?

Accepted Answer

x = 12

Answer

x = 6

Answer

x = 8

Answer

x = 10

Question 20

Which of the following is the solution to the inequality: x - 4 is less than 2?

Accepted Answer

x is less than 6

Answer

x is greater than 2

Answer

x is less than 2

Answer

x is greater than 6

Question 21

What is the value of y in the inequality: 2y - 5 is greater than 7?

Accepted Answer

y is greater than 6

Answer

y is less than 6

Answer

y is less than -6

Answer

y is greater than -6

Question 22

Which of the following is a two-step equation?

Accepted Answer

3x - 2 = 7

Answer

x + 5 = 10

Answer

2x + 5y = 10

Answer

x^2 + 2x - 3 = 0

Question 23

Which of the following represents the inequality "a number is greater than 5"?

Accepted Answer

x > 5

Answer

x < 5

Answer

x = 5

Answer

x is less than 5

Question 24

Translate the phrase "Twice a number, decreased by 4, equals 10" into an equation.

Accepted Answer

2x - 4 = 10

Answer

10 - 2x = 4

Answer

2x + 4 = 10

Answer

10 + 2x = 4

Question 25

The difference between two numbers is 8. If one number is x, what is the other number?

Accepted Answer

x - 8

Answer

x + 8

Answer

8 - x

Answer

x / 8

Question 26

Translate the verbal inequality 'The sum of x and 5 is less than 10' into an algebraic expression.

Accepted Answer

x + 5 < 10

Answer

10 > x + 5

Answer

10 < x + 5

Answer

x + 5 > 10

Question 27

Identify the linear equation among the following:

Accepted Answer

y = 2x + 5

Answer

y = 1/x

Answer

y = sin(x)

Answer

y = x^2 + 1

Question 28

Which of the following is equivalent to the inequality 2x - 5 > 11?

Accepted Answer

x > 8

Answer

x < 8

Answer

2x < 16

Answer

2x > 16

Question 29

Which of the following is an application of solving equations?

Accepted Answer

Determining the distance traveled by a car

Answer

Finding the volume of a sphere

Answer

Determining the area of a circle

Answer

Calculating the slope of a line

Question 30

Which inequality shows that a number, represented by 'x', is greater than or equal to 10?

Accepted Answer

x ≥ 10

Answer

x ≤ 10

Answer

x > 10

Answer

x < 10

Question 31

Sarah has $15.  She wants to buy a book that costs 'x' dollars.  Which inequality shows how much money she can spend on the book?

Accepted Answer

x ≤ 15

Answer

x < 15

Answer

x > 15

Answer

x ≥ 15

Question 32

Solve the equation: 4(x - 2) = 12

Accepted Answer

x = 5

Answer

x = 1

Answer

x = 2

Answer

x = 4

Question 33

Which number makes the inequality 5x + 3 > 18 true?

Accepted Answer

x = 4

Answer

x = 1

Answer

x = 2

Answer

x = 3

Question 34

What is the solution to the equation 2x - 5 = x + 3?

Accepted Answer

x = 8

Answer

x = 2

Answer

x = -2

Answer

x = 4

Question 35

Solve the equation: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = 1

Answer

x = 6

Answer

x = -3

Question 36

Which inequality shows that a number, represented by 'x', is less than or equal to 10?

Accepted Answer

x ≤ 10

Answer

x ≥ 10

Answer

x > 10

Answer

x < 10

Question 37

Solve for 'y' in the equation: 2y - 7 = 11

Accepted Answer

y = 9

Answer

y = 7

Answer

y = -2

Answer

y = 2

Question 38

Which number makes the inequality x + 4 > 9 true?

Accepted Answer

x = 6

Answer

x = 3

Answer

x = 5

Answer

x = 4

Question 39

A bakery sells cupcakes for $2 each. They need to make at least $100 to cover their costs. How many cupcakes do they need to sell to reach their goal?

Accepted Answer

50 or more

Answer

200 or more

Answer

25 or more

Answer

100 or more

Question 40

What is the first step in solving the equation 5x - 2 = 13?

Accepted Answer

Add 2 to both sides

Answer

Subtract 2 from both sides

Answer

Divide both sides by 5

Answer

Multiply both sides by 5

Question 41

Which of the following is NOT a solution to the inequality 2x - 3 ≤ 5?

Accepted Answer

x = 5

Answer

x = 1

Answer

x = 2

Answer

x = 3

Question 42

The perimeter of a square is 20 inches. What is the length of one side?

Accepted Answer

5 inches

Answer

4 inches

Answer

10 inches

Answer

2 inches

Question 43

Solve for 'm': 3(m + 2) = 15

Accepted Answer

m = 3

Answer

m = 5

Answer

m = 1

Answer

m = -1

Question 44

Sarah has $25 and wants to buy a book that costs $12. She also wants to buy some candy. How much money can she spend on candy?

Accepted Answer

x ≤ 13

Answer

x > 13

Answer

x ≥ 13

Answer

x = 13