Algebra for Beginners: Master the Basics of Algebra Online

Question 1

In a linear equation, the relationship between the variable and the constant is:

Accepted Answer

Linear

Answer

Exponential

Answer

Quadratic

Answer

Cubic

Question 2

Which of these is an algebraic expression?

Accepted Answer

x + 5

Accepted Answer

x^2

Answer

5x = 10

Answer

5

Question 3

Solve for x: 2x - 5 = 7

Accepted Answer

x = 6

Answer

x = 2

Answer

x = 8

Answer

x = 10

Question 4

Which equation has an infinite number of solutions?

Accepted Answer

x - 3 = x + 1

Answer

x + 3 = 7

Answer

x^2 = 9

Answer

x^2 + 1 = 0

Question 5

Solve the equation: 2(x - 3) = 10. What is the value of x?

Accepted Answer

x = 8

Answer

x = 1

Answer

x = 10

Answer

x = 12

Question 6

Simplify the expression 2x(x + 3) to get an equivalent expression.

Accepted Answer

2x^2 + 6x

Answer

x^2 + 3x

Answer

2x^2 - 6x

Answer

x^2 + 6x

Question 7

Which of these is a valid inequality?

Accepted Answer

-4x > 12

Accepted Answer

2y - 5 <= 10

Answer

3x + 5 = 0

Answer

x^2 - 2x + 1 = 0

Question 8

Which of the following is NOT an algebraic expression?

Accepted Answer

5 < x + 3

Answer

5x + 3

Answer

2x - 5

Answer

x^2 + 2x + 1

Question 9

Simplify the algebraic expression: 2x + 3y - 5x + 2y

Accepted Answer

-3x + 5y

Answer

x + 5y

Answer

-5x + y

Answer

5x + y

Question 10

To determine the number of solutions for the system of equations 2x + 3y = 6 and 4x + 6y = 12, which method should be used?

Accepted Answer

Find the determinant of the corresponding matrix.

Answer

Graph the system and count the intersection points.

Answer

Add the two equations and solve for x.

Question 11

Simplify the expression: 2x + 3y

Accepted Answer

2(x + y)

Answer

5xy

Answer

x + 3y

Answer

2x + y

Question 12

In the expression 2x^2 - 5x + 3, which term does not contain any variables?

Accepted Answer

3

Answer

2x^2

Answer

-5x

Answer

2x

Question 13

To solve the equation 2x + 5 = 15 using the method of isolating the variable, what should you do first?

Accepted Answer

Isolate the variable (x) by subtracting 5 from both sides of the equation

Answer

Subtract 5 from both sides of the equation

Answer

Divide both sides of the equation by 2

Question 14

To solve the inequality 2x + 5 < 15, what should you do first?

Accepted Answer

Subtract 5 from both sides

Answer

Divide both sides by 2

Answer

Multiply both sides by 2

Question 15

To solve the equation 3(x - 2) + 5 = 23, what should you do first?

Accepted Answer

Distribute the 3 to the terms inside the parentheses

Answer

Subtract 5 from both sides

Answer

Multiply 3 by x

Answer

Add 2 to both sides

Question 16

Which equation has a solution of x = 5?

Accepted Answer

x + 3 = 8

Answer

x^2 - 10 = 0

Answer

2x - 5 = 3(x + 1)

Answer

x^3 - 2 = 0

Question 17

To solve the system of equations 2x + 3y = 12 and x - y = 1 using the graphing method, which steps should you follow?

Accepted Answer

Plot both equations on a graph, locate their intersection point, and read the coordinates as the solution.

Answer

Substitute one equation into the other to solve for one variable, then substitute that value back to find the other variable.

Answer

Use a calculator to find the intersection point of the two equations.

Question 18

Which of these linear inequalities shows a shaded area that includes the point (0, 0)?

Accepted Answer

y ≤ -x + 3

Answer

y > 2x + 1

Answer

y ≥ 2x - 1

Answer

y < -2x + 1

Question 19

Factor the polynomial: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x - 3)²

Answer

(x + 9)²

Question 20

Write the equation of the line that has a slope of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 21

Determine the domain (set of input values) and range (set of output values) of the function: f(x) = |x - 2|.

Accepted Answer

Domain: all real numbers; Range: all non-negative real numbers

Answer

Domain: all real numbers greater than or equal to 2; Range: all real numbers

Answer

Domain: all non-negative real numbers; Range: all real numbers greater than or equal to 2

Question 22

Which of the following is NOT an algebraic expression?

Accepted Answer

3

Answer

3x + 2

Answer

x - 5

Answer

x^2

Question 23

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

Accepted Answer

x ≥ -5

Answer

x < -5

Answer

x > -5

Answer

x ≤ -5

Question 24

Which of the following is the graph of the equation y = 2x + 1? Describe the graph

Accepted Answer

Straight line with y-intercept 1 and slope 2

Answer

Straight line with y-intercept 2 and slope 1

Answer

Parabola with vertex (1, 2)

Answer

Circle with radius 2 centered at (1, 0)

Question 25

Which of the following graphs represents a quadratic function?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A hyperbola

Question 26

Solve the equation: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = 3

Answer

x = 6

Answer

x = 10

Question 27

Which graph accurately represents the inequality: y > 2x + 1?

Accepted Answer

[Image of a graph depicting y > 2x + 1]

Answer

[Image of a graph depicting y < 2x + 1]

Answer

[Image of a graph depicting y = 2x + 1]

Answer

[Image of a graph depicting y ≤ 2x + 1]

Question 28

Solve the equation: xy = 10

Accepted Answer

y = 10/x

Answer

y = x/10

Answer

y = 10 + x

Answer

y = 10 - x

Question 29

Determine the slope of the line passing through the points (2, 3) and (5, 7).

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 30

Which of the following mathematical expressions contains a variable?

Accepted Answer

2x + 5

Answer

five x five

Answer

x = 10

Answer

twenty minus three

Question 31

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

Accepted Answer

x

Answer

2

Answer

y + 3

Answer

100

Question 32

Factor the following expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

Cannot be factored

Answer

(x - 3)(x - 3)

Question 33

Solve the algebraic equation: 2x + 5 = 15

Accepted Answer

x = 10

Answer

x = 5

Answer

x = 15

Answer

x = 20

Question 34

A farmer has 120 feet of fencing to enclose a rectangular plot of land. If the width of the plot is x, which equation could be used to find the length of the plot?

Accepted Answer

2x + 2(120 - x) = 120

Answer

x + 120 = 120

Answer

x - 120 = 120

Answer

2x - 2(120 - x) = 120

Question 35

Solve for x: |x - 2| = 5

Accepted Answer

x = 7 or x = -3

Answer

x = 7 only

Answer

x = -3 only

Answer

No solution

Question 36

Which of the following is the graph of the equation y = 2x + 1?

Accepted Answer

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

Answer

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

Answer

A parabola with a vertex at (1, 2)

Answer

A circle with a center at (1, 2)

Question 37

Solve the inequality: x/4 is greater than 2

Accepted Answer

x is greater than 8

Answer

x is less than 8

Answer

x is less than 4

Answer

x is greater than 4

Question 38

A rectangular garden has a length of (x + 3) feet and a width of (x - 2) feet. What is its area in square feet?

Accepted Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

2x + 1

Answer

2x - 1

Question 39

Which equation is in slope-intercept form?

Accepted Answer

y = mx + b

Answer

y - mx = b

Answer

x = my + b

Answer

y = mx - b

Question 40

What is the slope of the line represented by the equation y + 2 = -3(x - 5)?

Accepted Answer

-3

Answer

2

Answer

3

Answer

5

Question 41

Which equation is a quadratic equation?

Accepted Answer

x^2 + 2x - 3 = 0

Answer

2x - 5 = 0

Answer

y = mx + b

Answer

x^3 + x - 1 = 0

Question 42

Solve for x: 2x^2 - 5x = 0

Accepted Answer

x = 0, x = 5/2

Answer

x = 1, x = -5/2

Answer

x = 0, x = 2.5

Answer

x = 1, x = 2.5

Question 43

Which value is in the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

x > 2

Answer

x >= 2

Answer

x < 2

Answer

x <= 2

Question 44

Identify the expression that represents the sum of variables x and y.

Accepted Answer

x + y

Answer

x - y

Answer

y - x

Answer

x / y

Question 45

Determine the equation of a line with a slope of 2 and a y-intercept of -3.

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = 2x + 3

Answer

y = -2x + 3

Question 46

Identify the variable in the equation 2x + 5 = 11.

Accepted Answer

x

Answer

2

Answer

5

Answer

11

Question 47

Classify the statement as an equation or inequality: x > 5

Accepted Answer

Inequality

Answer

Equation

Answer

Expression

Answer

Identity

Question 48

Simplify the expression: 3x(x + 2)

Accepted Answer

3x^2 + 6x

Answer

3x + 2

Answer

3x^2

Answer

3x^2 + 2

Question 49

Factor the expression: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

Cannot be factored

Answer

Factorization not applicable

Question 50

A rectangular garden has a length of 10 feet and a width of 5 feet. If the length is increased by 2 feet, what is the percentage increase in the area of the garden?

Accepted Answer

25%

Answer

20%

Answer

30%

Answer

35%

Question 51

Solve the following inequality: x - 3 > 5

Accepted Answer

x > 8

Answer

x > 2

Answer

x < 8

Answer

x < 2

Question 52

Factor the following expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

It's already in its simplest form

Answer

(x - 3)^2

Question 53

Express the quadratic formula

Accepted Answer

x = (-b ± √(b^2 - 4ac)) / 2a

Answer

x = (-b + √(b^2 - 4ac)) / 2a

Answer

x = (b ± √(b^2 + 4ac)) / 2a

Answer

x = (-b - √(b^2 - 4ac)) / 2a

Question 54

Which of the following is an algebraic expression?

Accepted Answer

2x + 5

Answer

5 - 2

Answer

the difference of two from five

Answer

the sum of five and two

Question 55

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

Accepted Answer

5 ≥ x

Answer

x ≥ 5

Answer

x ≠ 5

Answer

x = 5

Question 56

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

Accepted Answer

3x + 6

Answer

6x + 2

Answer

x + 6

Answer

3x + 2

Question 57

Which of the following is a solution to the equation 2x - 5 = 11?

Accepted Answer

8

Answer

12

Answer

10

Answer

6

Question 58

What is the slope of the line represented by the equation y = 2x + 1?

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 59

Which of the following expressions represents the area of a triangle?

Accepted Answer

1/2 × base × height

Answer

base - height

Answer

base + height

Answer

length × width

Question 60

Which of the following inequalities represents the statement 'The sum of x and 5 is greater than or equal to 10'?

Accepted Answer

x + 5 ≥ 10

Answer

10 ≥ x + 5

Answer

x - 5 ≥ 10

Answer

x + 5 ≤ 10

Question 61

What is the value of x in the equation 2x - 5 = 15?

Accepted Answer

10

Answer

5

Answer

20

Answer

15

Question 62

Which of the following is a solution to the inequality x + 3 < 7?

Accepted Answer

x < 4

Answer

x ≥ 4

Answer

x > 4

Answer

x ≤ 4

Question 63

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

Accepted Answer

(x = 3, y = 2)

Answer

(x = 2, y = 3)

Answer

(x = 1, y = 4)

Question 64

Identify the algebraic inequality from the following options:

Accepted Answer

x > 5

Answer

x + 5 = 10

Answer

x = 5

Answer

5x = 25