Linear Equations and Inequalities: Master the Basics with Engaging Quizzes

Question 1

Solve the inequality: 3x + 5 is greater than 14

Accepted Answer

x is greater than 3

Answer

x is less than 3

Answer

x is less than -3

Answer

x is greater than -3

Question 2

Graph the inequality **y < 2x + 1**.

Accepted Answer

Image of a shaded region below the line y = 2x + 1

Answer

Image of a shaded region above the line y = 2x + 1

Answer

Image of a shaded region to the left of the line y = 2x + 1

Answer

Image of a shaded region to the right of the line y = 2x + 1

Question 3

Which of the following is equivalent to the inequality **3x - 4 > 10**?

Accepted Answer

x > 4

Answer

x < 4

Answer

x > 14

Answer

x < 14

Question 4

Graph the equation **y = 2x - 3**.

Accepted Answer

Image of a line with a slope of 2 and a y-intercept of -3

Answer

Image of a line with a slope of 3 and a y-intercept of -2

Answer

Image of a line with a slope of -2 and a y-intercept of 3

Answer

Image of a line with a slope of -3 and a y-intercept of 2

Question 5

If the area of a rectangle is given by the expression 2x^2 + 5x - 3, and its width is 2x + 1, find the length of the rectangle.

Accepted Answer

x + 2

Answer

x - 2

Answer

2x - 1

Answer

2x + 1

Question 6

The sum of two consecutive odd integers is 110. Find the smaller integer.

Accepted Answer

55

Answer

54

Answer

56

Answer

57

Question 7

Which of the following is a linear function?

Accepted Answer

f(x) = 3x - 4

Answer

f(x) = x^2 + 2x - 1

Answer

f(x) = e^x

Answer

f(x) = sin(x)

Question 8

Find the slope of the line described by the equation: y = -2x + 5

Accepted Answer

-2

Answer

-1

Answer

1

Answer

2

Question 9

Determine the equation of the line passing through the point (2, 3) with a slope of -1:

Accepted Answer

y = -x + 1

Answer

y = -x + 5

Answer

y = x - 1

Answer

y = x + 5

Question 10

Find the solution to the inequality: 3x - 2 < 10

Accepted Answer

x < 4

Answer

x > 4

Answer

x < 2/3

Answer

x > 2/3

Question 11

Find the domain of the function: f(x) = 1 / (x - 2)

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

Only positive real numbers

Answer

Only negative real numbers

Question 12

Which of the following equations represents a horizontal line?

Accepted Answer

y = 5

Answer

y = 2x + 3

Answer

x = 3

Answer

y = -x + 2

Question 13

Solve the inequality: 2x - 5 < 11.

Accepted Answer

x < 8

Answer

x > 8

Answer

x < -8

Answer

x > -8

Question 14

Determine the slope of the line with the equation y = -3x + 4.

Accepted Answer

-3

Answer

3

Answer

4

Answer

-4

Question 15

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

Accepted Answer

(2, 3)

Answer

(3, 2)

Answer

(-3, 2)

Answer

(2, -3)

Question 16

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

Accepted Answer

7x + 3

Answer

7x - 3

Answer

8x - 3

Answer

8x + 3

Question 17

Find the solution to the equation: 2x - 7 = 15

Accepted Answer

x = 11

Answer

x = 4

Answer

x = 12

Answer

x = 22

Question 18

Which of the following is the graph of the inequality y > x + 2?

Accepted Answer

Shaded region above the line y = x + 2

Answer

Shaded region below the line y = x + 2

Answer

Shaded region to the left of the line y = x + 2

Answer

Shaded region to the right of the line y = x + 2

Question 19

A farmer has 400 meters of fencing to enclose a rectangular area. What is the maximum area that the farmer can enclose?

Accepted Answer

1600 square meters

Answer

400 square meters

Answer

800 square meters

Answer

3200 square meters

Question 20

What is the inverse of the function f(x) = 2x + 3?

Accepted Answer

f^-1(x) = (x - 3) / 2

Answer

f^-1(x) = (x + 3) / 2

Answer

f^-1(x) = 2x - 3

Answer

f^-1(x) = 2x + 3

Question 21

Solve the system of equations using either substitution or elimination: 2x + 3y = 13, x - 2y = 5

Accepted Answer

(x = 4, y = 1)

Answer

(x = 4, y = -1)

Answer

(x = -4, y = 1)

Answer

(x = -4, y = -1)

Question 22

Which of the following is NOT a characteristic of linear equations?

Accepted Answer

Multiple x-intercepts

Answer

Constant slope

Answer

Always straight lines

Answer

Represented by y = mx + c

Question 23

Determine the slope of the line passing through the points (2, 5) and (4, 9)

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 24

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

Accepted Answer

y = 3x - 2

Answer

y = 3x + 2

Answer

y = -3x - 2

Answer

y = -3x + 2

Question 25

A farmer has 200 meters of fencing to enclose a rectangular plot. If the width of the plot is half its length, determine the maximum area the farmer can enclose.

Accepted Answer

1250 square meters

Answer

1000 square meters

Answer

1500 square meters

Answer

1750 square meters

Question 26

Identify the linear function.

Accepted Answer

f(x) = 2x + 5

Answer

f(x) = x^2 + 1

Answer

f(x) = sin(x)

Answer

f(x) = e^x

Question 27

Find the slope of the line perpendicular to the line 3x - 2y = 6

Accepted Answer

-2/3

Answer

1.5

Answer

2/3

Answer

-1.5

Question 28

Find the equation of the perpendicular bisector of the line segment joining the points (2, 3) and (6, 9).

Accepted Answer

y = -x + 5

Answer

y = x - 5

Answer

y = -x + 7

Answer

y = x - 7

Question 29

Solve the following equation for x: 2x + 5 = 11.

Accepted Answer

x = 3

Answer

x = 2

Answer

x = -3

Answer

x = 4

Question 30

Which of the following is NOT a solution to the inequality x < 5?

Accepted Answer

x = 6

Answer

x = -2

Answer

x = 4

Answer

x = 0

Question 31

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

Accepted Answer

x = 3, y = 2

Answer

x = 1, y = 4

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Question 32

Write the equation of the line with a slope of -1 and a y-intercept of 2.

Accepted Answer

y = -x + 2

Answer

y = x + 2

Answer

y = -2x + 1

Answer

y = 2x - 1

Question 33

Solve the equation 3x + 5 = 14 for x.

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 5

Answer

x = 4

Question 34

What is the solution to the inequality 2x - 7 < 5?

Accepted Answer

x < 6

Answer

x ≤ 6

Answer

x > 6

Answer

x ≥ 6

Question 35

Which of the following points lies on the line represented by the equation y = 2x + 1?

Accepted Answer

(2, 5)

Answer

(3, 2)

Answer

(2, 3)

Answer

(1, 2)

Question 36

A phone company charges a £10 monthly fee plus £0.05 per minute for calls.  Which equation represents the total monthly cost (C) for x minutes of calls?

Accepted Answer

C = 0.05x + 10

Answer

C = 10x + 0.05

Answer

C = 10x

Answer

C = 0.05x

Question 37

Solve the system of equations: 2x + y = 7 and x - y = 1

Accepted Answer

x = 2, y = 3

Answer

x = 1, y = 2

Answer

x = 3, y = 2

Answer

x = 3, y = 1

Question 38

Which of the following inequalities represents the shaded region in the graph?

Accepted Answer

y > x - 1

Answer

y < x - 1

Answer

y ≥ x - 1

Question 39

A bakery sells cookies for £1.50 each and brownies for £2 each. Sarah wants to spend no more than £12 on treats. If x represents the number of cookies and y represents the number of brownies, which inequality represents this situation?

Accepted Answer

1.5x + 2y ≤ 12

Answer

1.5x + 2y ≥ 12

Answer

2x + 1.5y ≤ 12

Answer

2x + 1.5y ≥ 12

Question 40

Find the slope of the line passing through the points (1, 2) and (3, 6).

Accepted Answer

2

Answer

-1/2

Answer

1/2

Answer

-2

Question 41

Determine the y-intercept of the line represented by the equation 4x - 2y = 8.

Accepted Answer

(0, -4)

Answer

(2, 0)

Answer

(-2, 0)

Answer

(0, 4)

Question 42

Solve for x: 3x - 5 = 16

Accepted Answer

x = 7

Answer

x = -11

Answer

x = 11

Answer

x = -7

Question 43

What is the solution to the inequality 2x + 4 < 10?

Accepted Answer

x < 3

Answer

x > 3

Answer

x ≤ 3

Answer

x ≥ 3

Question 44

Which point lies on the line represented by the equation y = 2x - 1?

Accepted Answer

(2, 3)

Answer

(1, 1)

Answer

(0, 2)

Answer

(3, 5)