Expressions and Equations: Master Algebra's Building Blocks

Question 1

Solve for x: 2(x - 3) - 5 = 15

Accepted Answer

x = 13

Answer

x = 5

Answer

x = -5

Question 2

Determine if the equations 2(x - 3) = 6 and x - 3 = 3 are equivalent.

Accepted Answer

Yes, as both equations have the same solution, x = 3.

Answer

No, as the equations have different numerical coefficients.

Answer

No, as the equations have different intercepts.

Answer

No, as the graphs of the equations are not identical.

Question 3

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

Accepted Answer

2x^2 - 10x + 3x - 15

Answer

2x^2 + 3x - 10x - 15

Answer

2x^2 - 7x

Question 4

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

Accepted Answer

x = 4

Answer

x = 8

Answer

x = 10

Answer

x = 12

Question 5

The equation y = 3x + 5 represents a straight line. What is the slope of this line?

Accepted Answer

3

Answer

1

Answer

5

Answer

-3

Question 6

What is the simplified form of the expression 2x + 3y - 5?

Accepted Answer

2x + y - 5

Answer

5x + y - 5

Answer

x + 2y - 5

Answer

2x + 3y

Question 7

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

Accepted Answer

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

Answer

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

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 8

Solve for x in the following equation:

```
(x + 2)^2 - 5 = 12
```

Accepted Answer

x = 2 or x = -7

Answer

x = 3 or x = -8

Answer

x = 4 or x = -9

Answer

x = 5 or x = -10

Question 9

Graph the equation: y = 2x - 1

Accepted Answer

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

Answer

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

Answer

A parabola with a vertex at (1, -2)

Answer

A circle with a center at (0, -1)

Question 10

Solve the inequality: x - 5 > 2

Accepted Answer

x > 7

Answer

x < 7

Answer

x > -7

Answer

x < -7

Question 11

Graph the inequality: y < x + 2

Accepted Answer

The region below the line y = x + 2

Answer

The region above the line y = x + 2

Answer

The region on the line y = x + 2

Answer

The entire coordinate plane

Question 12

Which of the following is the slope-intercept form of the equation of a line?

Accepted Answer

y = mx + b

Answer

y = mx - b

Answer

x = my + b

Answer

x = my - b

Question 13

Find the equivalent expression for: (2x + 3)(x - 1)

Accepted Answer

2x^2 + x - 3

Answer

2x^2 - x - 3

Answer

2x^2 + 5x - 3

Answer

2x^2 - 5x - 3

Question 14

Determine the equation of the circle with center (2, -3) and radius 5:

Accepted Answer

(x - 2)^2 + (y + 3)^2 = 25

Answer

(x + 2)^2 + (y - 3)^2 = 25

Answer

(x - 2)^2 + (y + 3)^2 = 5

Answer

(x + 2)^2 + (y - 3)^2 = 5

Question 15

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

Accepted Answer

x - 4

Answer

x + 8

Answer

5x + 4

Answer

5x - 4

Question 16

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 17

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

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = -2, y = -3

Answer

x = -3, y = -2

Question 18

Find the domain of the function: f(x) = 1/(x - 3)

Accepted Answer

All real numbers except 3

Answer

All real numbers

Answer

All real numbers greater than 3

Answer

All real numbers less than 3

Question 19

Which of the following expressions is equivalent to the result of multiplying the binomials (2x + 3) and (x - 5)?

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 - 7x + 15

Answer

-2x^2 - 7x - 15

Answer

2x^2 + 7x + 15

Question 20

Find the slope of the line represented by the equation y = 2x + 1.

Accepted Answer

2

Answer

-2

Answer

1

Question 21

Simplify the expression: rac{2x^2y}{4xy^2}

Accepted Answer

rac{x}{2y}

Answer

2rac{x}{y}

Answer

rac{y}{2x}

Answer

2rac{y}{x}

Question 22

Graph the equation y = 2x - 1 on the coordinate plane. Describe the graph (e.g., slope, y-intercept).

Accepted Answer

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

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 -1)

Question 23

Which of the following is NOT a property of equality?

Accepted Answer

If a = b, then b ≠ a.

Answer

If a = b, then a + c = b + c.

Answer

If a = b, then ac = bc.

Answer

If a = b, then a - c = b - c.

Question 24

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

Accepted Answer

8x + 11

Answer

10x - 3

Answer

6x - 2

Answer

12x + 5

Question 25

Which of the following is 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 26

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

Accepted Answer

5x - 6

Answer

7x - 2

Answer

3x - 6

Question 27

Which of the following describes the line represented by the equation y = -x + 3?

Accepted Answer

A line with a slope of -1 and a y-intercept of 3.

Answer

A line with a slope of -1 and a y-intercept of -3.

Answer

A line with a slope of 1 and a y-intercept of 3.

Answer

A line with a slope of 1 and a y-intercept of -3.

Question 28

Which expression represents the perimeter of a rectangle with length x and width y?

Accepted Answer

2x + 2y

Answer

xy

Answer

x + y

Answer

x/y

Question 29

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4 = 0

Answer

2x - 3 = 0

Answer

x^3 + 2 = 0

Answer

x + 4 = 0

Question 30

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)(x - 3)

Answer

(x - 9)(x - 9)

Question 31

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

Accepted Answer

(3, 2)

Answer

(1, 4)

Answer

(2, 3)

Answer

(4, 1)

Question 32

Which equation represents a line with a slope of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = x - 2

Answer

y = 1 - 2x

Answer

y = -2x + 1

Question 33

What is the equation of a line that passes through the point (2, 5) and has a slope of 3?

Accepted Answer

y = 3x + 1

Answer

y = 2x - 3

Answer

y = 3x - 1

Answer

y = 2x + 5

Question 34

A rectangular garden has a length that is 5 units more than its width. If the perimeter of the garden is 30 units, find its width.

Accepted Answer

5 units

Answer

15 units

Answer

10 units

Answer

20 units

Question 35

Simplify the expression: (3x²)³

Accepted Answer

27x⁶

Answer

9x⁴

Answer

27x⁴

Answer

9x⁶

Question 36

A train travels at a speed of 80 kilometers per hour. Express the distance, d, traveled in t hours as an equation.

Accepted Answer

d = 80t

Answer

d = t/80

Answer

t = d/80

Answer

t = 80d

Question 37

Combine like terms: 4x - 2y + 3x + 5y

Accepted Answer

7x + 3y

Answer

7x - 3y

Answer

11x - 7y

Answer

-x + 7y

Question 38

Solve for x: 5x - 15 = 20

Accepted Answer

x = 7

Answer

x = 5

Answer

x = 10

Answer

x = 3

Question 39

Which of the following is a quadratic equation?

Accepted Answer

y = x² + 2x - 1

Answer

y = 2x + 3

Answer

y = √x

Answer

y = 1/x

Question 40

The area of a rectangular garden is 24 square meters. If the length is 6 meters, find its width.

Accepted Answer

4 meters

Answer

12 meters

Answer

8 meters

Answer

16 meters

Question 41

What is the y-intercept of the line represented by the equation 2x + 3y = 6?

Accepted Answer

2

Answer

-2

Answer

-3

Answer

3

Question 42

Which of the following represents the graph of the equation y = 2x - 1?

Accepted Answer

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

Answer

A line with a negative slope passing through the point (1, -2)

Answer

A parabola opening upwards

Question 43

Solve the equation: 2x + 7 = 15

Accepted Answer

x = 4

Answer

x = 11

Answer

x = 8

Answer

x = 1

Question 44

Which of the following is an equation?

Accepted Answer

3x - 5 = 10

Answer

2x + 7

Answer

4 + 3z

Answer

5y - 2

Question 45

Find the slope of the line represented by the equation y = 2x + 1

Accepted Answer

2

Answer

3

Answer

-2

Question 46

What is the equation of the line passing through the points (1, 2) and (3, 6)?

Accepted Answer

y = x + 1

Answer

y = -2x + 4

Answer

y = 2x

Answer

y = 3x - 1

Question 47

Solve the inequality 2x - 5 < 11.

Accepted Answer

x < 8

Answer

x > 8

Answer

x < 3

Answer

x > 3

Question 48

The perimeter of a rectangle is 20 cm. If the length is 7 cm, what is the width?

Accepted Answer

6.5 cm

Answer

10 cm

Answer

13 cm

Answer

7 cm

Question 49

Which of the following is a root of the equation x^2 - 4 = 0?

Accepted Answer

x = 2 or x = -2

Answer

x = -1

Answer

x = 0

Answer

x = 1

Question 50

The graph of the equation y = -x + 2 will have a:

Accepted Answer

Negative slope and a y-intercept of 2

Answer

Positive slope and a y-intercept of 2

Answer

Negative slope and a y-intercept of -2