Expressions and Equations: Master Algebra Basics

Question 1

Translate the phrase 'the sum of a number and twice another number' into an algebraic expression.

Accepted Answer

x + 2y

Answer

x - 2y

Answer

2x + y

Answer

x * 2y

Question 2

Determine the slope and y-intercept of the equation y = -2x + 5.

Accepted Answer

Slope: -2, y-intercept: 5

Answer

Slope: 5, y-intercept: -2

Answer

Slope: 2, y-intercept: -5

Answer

Slope: -5, y-intercept: 2

Question 3

Translate the sentence into an algebraic inequality: The total, represented by x, is at most 10 when 5 is added to it.

Accepted Answer

x + 5 ≤ 10

Answer

x + 5 > 10

Answer

x - 5 ≤ 10

Answer

x - 5 > 10

Question 4

When we multiply both sides of the equation 2x + 3 = 7 by -1/2, what will happen to the solution?

Accepted Answer

The solution will be halved.

Answer

The solution will be doubled.

Answer

The solution will be negated.

Answer

The equation will no longer be linear.

Question 5

In the equation '5 + x = 10', what does the equal sign indicate?

Accepted Answer

The equal sign means that '5 + x' and '10' have the same value when 'x' has a specific value.

Answer

The equal sign shows that '5 + x' is always equal to '10', no matter what the value of 'x' is.

Answer

The equal sign means that 'x' is equal to '5'.

Answer

The equal sign is used to separate the two sides of the equation.

Question 6

Use the distributive property to simplify the expression: 3(2x + 4)

Accepted Answer

6x + 12

Answer

x + 12

Answer

6x + 8

Answer

3x + 4

Question 7

Determine the equation of the line that is perpendicular to the line y = 2x - 3 and passes through the point (1, 4).

Accepted Answer

y = -1/2x + 3.5

Answer

y = 2x - 7

Answer

y = -2x + 5

Answer

y = 1/2x + 3

Question 8

Which of the following is the equation of a line parallel to y = 2x - 1?

Accepted Answer

y = 2x

Answer

y = 2x + 2

Answer

y = -2x - 1

Answer

y = -2x + 2

Question 9

Solve the linear equation: 2x + 5 = 13

Accepted Answer

x = 6

Answer

x = 2

Answer

x = 4

Answer

x = 8

Question 10

Which of the following equations has a slope of -3?

Accepted Answer

y = -3x + 2

Answer

y = 3x - 2

Answer

y = -2x + 3

Answer

y = 2x - 3

Question 11

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

Accepted Answer

2x + 7y

Answer

4x + 3y

Answer

2x - 3y

Answer

4x - 3y

Question 12

Solve the equation: 2x - 5 = 15

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 13

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 14

Which of the following is the midpoint of the line segment connecting the points (1, 4) and (7, 10)?

Accepted Answer

(5, 7)

Answer

(4, 7)

Answer

(4, 8)

Answer

(5, 8)

Question 15

Find the value of x that makes the following equation true: 3(x - 2) = 9

Accepted Answer

4

Answer

2

Answer

3

Answer

5

Question 16

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 17

Apply the distributive property to expand the expression: 3(2x - 5)

Accepted Answer

6x - 15

Answer

6x - 5

Answer

3x - 15

Answer

3x - 5

Question 18

Which of the following expressions is equivalent to 3 times the sum of x and 2?

Accepted Answer

3x + 6

Answer

3x + 2

Answer

x + 6

Answer

x + 2

Question 19

Write an inequality that represents the statement: 'The total of x and 3 is greater than or equal to 10.'

Accepted Answer

x + 3 ≥ 10

Answer

x + 3 ≤ 10

Answer

10 ≥ x + 3

Answer

10 ≤ x + 3

Question 20

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 21

Which of the following is an example of a linear function?

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = sin(x)

Answer

y = e^x

Question 22

What is the x-intercept of the line y = 3x - 2?

Accepted Answer

2/3

Answer

-2/3

Answer

3

Answer

-3

Question 23

When solving the system of equations using matrices, which step is not valid?
2x + y = 5
x - y = 1

Accepted Answer

Add the first row and third row of the matrix.

Answer

Write the system in matrix form.

Answer

Find the determinant of the coefficient matrix.

Answer

Use row operations to transform the matrix into an upper triangular matrix.

Question 24

What is the correct way to find the value of the function f(x) = 2x + 5 when x is 3?

Accepted Answer

f(3)

Answer

3f(x)

Answer

f(3x)

Answer

3 + f(x)

Question 25

Translate the following verbal expression into an algebraic expression: 
The sum of a number and 5

Accepted Answer

x + 5

Answer

x - 5

Answer

5 - x

Answer

x ^ 5

Question 26

Solve the system of equations: 2x + y = 10, x - y = 2.

Accepted Answer

x = 4, y = 2

Answer

x = 2, y = 4

Answer

x = -4, y = -2

Answer

x = 6, y = 4

Question 27

Choose the correct graph for the linear equation: y = 2x + 1

Accepted Answer

A line passing through the point (0, 1) with a slope of 2

Answer

A line passing through the point (1, 0) with a slope of 2

Answer

A line passing through the point (0, 1) with a slope of 1

Answer

A line passing through the point (1, 0) with a slope of 1

Question 28

Which symbol does NOT represent an inequality?

Accepted Answer

=

Answer

>

Answer

<

Answer

≥

Question 29

Calculate the value of the expression: 2x² - 3y when x equals 2 and y equals 1

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 30

Consider the following mathematical expressions: 2x + 5, x = 5, y > 10, and the sum of two numbers. Which one is an algebraic expression?

Accepted Answer

2x + 5

Answer

x = 5

Answer

y > 10

Answer

The sum of two numbers

Question 31

How would you graph the line with the equation y = 2x + 1?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

A rectangular garden has a length of 12 feet and a width of 18 feet. What is the diagonal distance across the garden, from one corner to the opposite corner?

Accepted Answer

21.6 feet

Answer

6 feet

Answer

15 feet

Question 33

How do the slope and intercept affect the graph of a linear function?

Accepted Answer

The slope of the line determines how steep the line is, and the intercept determines where the line crosses the y-axis.

Answer

The intercept of the line determines how steep the line is, and the slope determines where the line crosses the y-axis.

Answer

The slope and intercept of a line have no effect on the graph of the line.

Question 34

Simplify the expression: √(x^6 / y^4)

Accepted Answer

x^3 / y^2

Answer

x^3 / y^4

Answer

x^6 * y^4

Question 35

Find the vertex of the parabola represented by the function y = 2x² - 3x + 1.

Accepted Answer

(-3/4, 13/8)

Answer

(-1, 1)

Answer

(0, 1)

Answer

(1, 0)

Question 36

Which inequality represents the solution to: x + 3 > 7?

Accepted Answer

x > 4

Answer

x < -4

Answer

x < 4

Answer

x > -4

Question 37

Write the equation of the 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 38

Which expression represents the same value as 3x + 5?

Accepted Answer

5 + 3x

Answer

x + 3 + 5

Answer

3x * 5

Answer

3x - 5

Question 39

Solve for x in the equation: 2x - 5 = 11

Accepted Answer

8

Answer

10

Answer

6

Question 40

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

Accepted Answer

x ≥ 5

Answer

x < 5

Answer

5 ≤ x

Question 41

Which expression represents the area of a rectangle with a length of 'x' units and a width of '3x' units?

Accepted Answer

3x^2

Answer

2x + 3x

Answer

x + 3x

Answer

x^2 + 3x^2

Question 42

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

Accepted Answer

(3, 2)

Answer

(1, 4)

Answer

(2, 3)

Question 43

Identify which expression is equivalent to 3(x + 2):

Accepted Answer

3x + 6

Answer

9x + 2

Answer

x + 6

Answer

6x + 3

Question 44

Which of the following expressions is a rational expression?

Accepted Answer

2x/(x - 1)

Answer

x^2 + 1

Answer

√x

Answer

1/0

Question 45

Apply the distributive property to expand the following expression: 3(2x - 5)

Accepted Answer

6x - 15

Answer

3x - 5

Answer

3x - 15

Answer

6x - 5

Question 46

Which of these is a linear equation with one variable?

Accepted Answer

2x + 5 = 11

Answer

x^2 + 3x + 2 = 0

Answer

y = x^3 - 2

Question 47

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

Accepted Answer

5x - 4

Answer

x + 5

Answer

6x - 6

Question 48

What is the solution to the equation: x + 7 = 12?

Accepted Answer

5

Answer

19

Answer

12

Answer

7

Question 49

Which graph represents the equation y = 2x + 1?

Accepted Answer

(Image of a line with a slope of 2 and a y-intercept of 1)

Answer

(Image of a line with a slope of 1 and a y-intercept of 2)

Answer

(Image of a parabola)

Question 50

Solve the inequality: x - 3 < 7

Accepted Answer

x < 10

Answer

x > 4

Answer

x > 10

Answer

x < 4

Question 51

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

Accepted Answer

x^2 - x - 6

Answer

x^2 + 5x + 6

Answer

x^2 - 5x + 6

Answer

x^2 + x - 6

Question 52

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

Accepted Answer

(x = 3, y = 2)

Answer

(x = 4, y = 1)

Answer

(x = 2, y = 3)

Answer

(x = 1, y = 4)

Question 53

Which of these is a real-world application of solving linear equations?

Accepted Answer

Finding the break-even point in a business

Answer

Cooking a meal

Answer

Winning a lottery

Answer

Predicting the weather

Question 54

Simplify the expression: (2x^2 + 3x - 5) - (x^2 - 2x + 1)

Accepted Answer

x^2 + 5x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x + 6

Answer

x^2 - 5x + 6

Question 55

What are the solutions to the equation: |x - 2| = 5?

Accepted Answer

x = 7 or x = -3

Answer

x = 2 or x = -2

Answer

x = 3 or x = -7

Answer

x = 5 or x = -5

Question 56

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

Accepted Answer

2x + 1

Answer

4x + 1

Answer

x + 1

Answer

2x - 5

Question 57

Graph the line represented by the equation: y = 2x + 1

Accepted Answer

(0, 1) and (1, 3)

Answer

(0, 0) and (1, 2)

Answer

(-1, 1) and (0, 2)

Answer

(0, 2) and (1, 4)

Question 58

Find the slope of the line that passes through the points (2, 5) and (4, 9)

Accepted Answer

2

Answer

1

Answer

-2

Answer

-1

Question 59

Solve the inequality: 2x - 5 > 7

Accepted Answer

x > 6

Answer

x < 6

Answer

x > -6

Answer

x < -6

Question 60

Which of the following expressions is a polynomial?

Accepted Answer

2x^3 + 5x^2 - 7x + 1

Answer

sin(x) + cos(x)

Answer

x^2 + √x - 3

Answer

1/x + 2x^2

Question 61

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 1)(x - 9)

Answer

(x + 9)(x - 9)

Question 62

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

Accepted Answer

(3, 2)

Answer

(1, 4)

Answer

(2, 3)

Answer

(4, 1)

Question 63

Simplify the expression: 3x + 2x - 5

Accepted Answer

5x - 5

Answer

5x + 5

Answer

x - 5

Answer

x + 5

Question 64

Solve for x: x + 5 = 12

Accepted Answer

7

Answer

12

Answer

5

Answer

17