Linear Equations and Inequalities: Master the Basics with Interactive Quizzes

Question 1

Find the value of x that makes the inequality true: 2x + 5 is greater than 13

Accepted Answer

x is greater than 4

Answer

x is less than 4

Answer

x is greater than -4

Answer

x is less than -4

Question 2

Which of the following is the equation of a line with a gradient of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = -2x + 3

Answer

y = 3 - 2x

Question 3

Find the solution to the inequality: 2x + 5 is greater than 11

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 4

Identify the type of graph for the quadratic equation: y = -2x^2 + 4x + 1

Accepted Answer

A parabola opening downwards

Answer

A parabola opening upwards

Answer

A straight line with a positive gradient

Answer

A straight line with a negative gradient

Question 5

Select the graph that represents the inequality y > 2x + 1.

Accepted Answer

A line with gradient 2 and y-intercept 1, shaded above the line.

Answer

A line with gradient 1/2 and y-intercept 1, shaded below the line.

Answer

A line with gradient 2 and y-intercept -1, shaded below the line.

Answer

A line with gradient 1/2 and y-intercept -1, shaded above the line.

Question 6

Choose the equivalent inequality for 2x - 5 < 11.

Accepted Answer

x < 8

Answer

x > 8

Answer

x < -8

Answer

x > -8

Question 7

Identify the gradient of the line y = -3x + 2.

Accepted Answer

-3

Answer

3

Answer

2

Answer

-2

Question 8

Identify the vertex of the parabola y = x^2 - 4x + 3.

Accepted Answer

(2, -1)

Answer

(2, 1)

Answer

(-2, 1)

Answer

(-2, -1)

Question 9

If the line y = mx + c is perpendicular to the line y = 2x + 1, what is the value of m?

Accepted Answer

m = -1/2

Answer

m = -2

Answer

m = 1/2

Answer

m = 2

Question 10

Find the midpoint of the line segment joining the points (2, 3) and (6, 7).

Accepted Answer

(4, 5)

Answer

(5, 4)

Answer

(6, 8)

Answer

(8, 6)

Question 11

The area of the triangle formed by the coordinate axes and the line y = 2x + 1 is:

Accepted Answer

1/2

Answer

1

Answer

2

Answer

4

Question 12

What is the equation of the line with a gradient of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = x + 2

Answer

y = x - 3

Question 13

Solve for x: |x - 2| = 5

Accepted Answer

x = 3 or x = -3

Answer

x = 7 or x = -7

Answer

x = 3 only

Answer

x = -3 only

Question 14

Which equation is perpendicular to the line y = 2x + 1?

Accepted Answer

y = -1/2x + 1

Answer

y = -2x + 1

Answer

y = 2x - 1

Answer

y = 1/2x - 1

Question 15

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

Accepted Answer

2

Answer

1

Answer

-1

Answer

-2

Question 16

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 17

Solve the linear equation: **2x + 5 = 13**

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7

Question 18

Which equation represents the line passing through the points **(2, 5) and (4, 9)**?

Accepted Answer

y = 2x + 1

Answer

y = 2x - 1

Answer

y = x + 3

Answer

y = x - 3

Question 19

Find the x-intercept of the line **y = 4x - 8**

Accepted Answer

-2

Answer

-1

Answer

1

Answer

2

Question 20

Determine if the point (2, 3) lies in the solution region of the system of inequalities: x < 4 and y ≥ 2.

Accepted Answer

Yes

Answer

No

Question 21

Find the slope of the line passing through the points (1, 2) and (3, 8).

Accepted Answer

3

Answer

2

Answer

6

Answer

4

Question 22

Which graph represents the inequality y > 2x - 1?

Accepted Answer

A straight line with a slope of 2 and a y-intercept of -1, shaded above the line

Answer

A straight line with a slope of -2 and a y-intercept of 1, shaded below the line

Answer

A parabola with a vertex at (2, 1)

Answer

A circle with a center at (2, 1) and a radius of 1

Question 23

Graph the inequality: y > 2x - 1. Select the correct representation.

Accepted Answer

A line with a positive gradient above the line y = 2x - 1

Answer

A line with a positive gradient below the line y = 2x - 1

Answer

A line with a negative gradient above the line y = 2x - 1

Answer

A line with a negative gradient below the line y = 2x - 1

Question 24

Find the domain of the function f(x) = sqrt(x - 2)?

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

All real numbers

Question 25

If the slope of a line is -3, what is the gradient of the perpendicular line?

Accepted Answer

-1/3

Answer

3

Answer

1/3

Answer

-3

Question 26

Which of the following is the graph of the inequality y > 2x - 1? Choose the correct option.

Accepted Answer

A line with a positive gradient, dashed below and solid above

Answer

A line with a positive gradient, dashed above and solid below

Answer

A line with a negative gradient, dashed below and solid above

Answer

A line with a negative gradient, dashed above and solid below

Question 27

Find the solution to the system of equations: x + y = 5 and x - y = 1. Select the correct option.

Accepted Answer

x = 3, y = 2

Answer

x = 2, y = 3

Answer

x = 4, y = 1

Answer

x = 1, y = 4

Question 28

Identify the statement that is NOT a property of linear equations. Select the correct option.

Accepted Answer

They always have positive gradients

Answer

They can have multiple solutions

Answer

Their graphs are always straight lines

Answer

They can be expressed in the form Ax + By = C

Question 29

Solve the inequality: 2x - 3 > 5. Choose the correct answer.

Accepted Answer

x > 4

Answer

x < 4

Answer

x > -4

Answer

x < -4

Question 30

Find the equation of the line passing through the points (2, 5) and (-1, 1) in the form y = mx + c.

Accepted Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = -x + 3

Answer

y = -2x + 5

Question 31

Solve the inequality 2x - 5 > 7 and express the solution in interval notation.

Accepted Answer

x > 6

Answer

x < 6

Answer

x > -6

Answer

x < -6

Question 32

The sum of two numbers is 15. One number is 3 less than the other. Find the two numbers.

Accepted Answer

9 and 12

Answer

6 and 9

Answer

12 and 15

Answer

15 and 18

Question 33

Solve the linear equation: 3x + 5 = 14

Accepted Answer

x = 7

Answer

x = 3

Answer

x = 5

Answer

x = 10

Question 34

Which graph represents the linear inequality y > 2x - 1?

Accepted Answer

A straight line with a solid boundary above it

Answer

A straight line with a dashed boundary below it

Answer

A parabola opening upwards

Answer

A parabola opening downwards

Question 35

Solve the system of linear equations:
y = 2x - 1
y = x + 5

Accepted Answer

x = 3, y = 5

Answer

x = 2, y = 3

Answer

x = 4, y = 7

Answer

x = 5, y = 9

Question 36

Simplify the algebraic expression: 5(x - 2)

Accepted Answer

5x - 2

Answer

5x + 2

Answer

x - 10

Answer

x + 10

Question 37

Find the y-intercept of the line represented by the equation y = -2x + 5

Accepted Answer

5

Answer

-2

Answer

2

Answer

-5

Question 38

Solve the equation involving absolute value: |x - 3| = 5

Accepted Answer

x = 2 or x = 8

Answer

x = -2 or x = -8

Answer

x = 8

Answer

x = 2

Question 39

Write down the equation of the line with a gradient of -3 and a y-intercept of 2

Accepted Answer

y = -3x + 2

Answer

y = 2x - 3

Answer

y = 3x - 2

Answer

y = -2x + 3

Question 40

Which of the following is NOT a step in solving the equation 3(x + 2) - 5 = 10?

Accepted Answer

Divide both sides by 2

Answer

Distribute the 3

Answer

Combine like terms

Answer

Subtract 5 from both sides

Question 41

Which system of equations has no solution?

Accepted Answer

x + 2y = 6, 2x + 4y = 12

Answer

x + y = 5, x - y = 1

Answer

2x + y = 4, x - y = 2

Answer

3x - y = 9, x + 2y = 14

Question 42

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 43

Which of the following is a linear equation?

Accepted Answer

y = 3x - 2

Answer

x^2 + y = 5

Answer

x * y = 10

Answer

sin(x) = cos(y)

Question 44

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

Accepted Answer

y = 2x + 1

Answer

y = x + 3

Answer

y = 2x - 1

Answer

y = x - 3

Question 45

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 46

Simplify the inequality 2x - 5 > 3:

Accepted Answer

x > 4

Answer

x < 4

Answer

x > -4

Answer

x < -4

Question 47

Which of the following is NOT a linear equation?

Accepted Answer

y = x^2 + 1

Answer

y = 3x + 2

Answer

3x - 5y = 10

Answer

2x + y = 7

Question 48

Which of the following is the equation of the line with a slope of -2 and passing through the point (1, 3)?

Accepted Answer

y = -2x + 5

Answer

y = -2x + 7

Answer

y = 2x + 1

Answer

y = 2x + 3

Question 49

Solve the inequality: x + 3 ≤ 7

Accepted Answer

x ≤ 4

Answer

x ≥ 4

Answer

x < 4

Answer

x > 4

Question 50

Find the value of k for which the line 2x + ky = 5 is perpendicular to the line y = 3x + 1:

Accepted Answer

k = -1

Answer

k = 2

Answer

k = 3

Answer

k = 4

Question 51

Identify the inequality in the following options:

Accepted Answer

x + 3 > 7

Answer

2x = 5

Answer

y - 2 = 0

Answer

5x - 1 = 10

Question 52

Graph the linear inequality: y < 2x + 1

Accepted Answer

[Image of a graph with a line y = 2x + 1 and shaded area below the line]

Answer

[Image of a graph with a line y = 2x + 1 and shaded area above the line]

Answer

[Image of a graph with a line y = 2x - 1 and shaded area below the line]

Answer

[Image of a graph with a line y = 2x - 1 and shaded area above the line]

Question 53

Find the gradient of the line represented by the equation: y = 3x - 2

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 54

Solve the inequality: 3(x - 2) > 6

Accepted Answer

x > 2

Answer

x < 0

Answer

x < 2

Answer

x > 0

Question 55

Solve the equation for y: ax + by = c

Accepted Answer

y = (c - ax) / b

Answer

y = (c + ax) / b

Answer

y = (ax - c) / b

Answer

y = (c / a) - bx

Question 56

Find the solution to the linear equation: 2x + 5 = 15

Accepted Answer

x = 10

Answer

x = 5

Answer

x = 15

Answer

x = 20

Question 57

Determine the solution to the system of equations: 2x + y = 10 and x - y = 2

Accepted Answer

x = 4, y = 2

Answer

x = 2, y = 4

Answer

x = 3, y = 3

Answer

x = 3, y = 4

Question 58

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

Accepted Answer

y = -2x + 3

Answer

y = 3x - 2

Answer

y = 2x + 3

Answer

y = -3x + 2

Question 59

Find the vertex of the parabola: y = -x^2 + 4x - 3

Accepted Answer

(2, 5)

Answer

(-2, 5)

Answer

(2, -3)

Answer

(-2, -3)

Question 60

Which of the following equations represents a linear relationship?

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = sin(x)

Answer

y = e^x

Question 61

Formulate the system of equations that models the following situation: The sum of two numbers is 10.

Accepted Answer

x + y = 10
y = 10 - x

Answer

x + y = 10
x - y = 0

Answer

x^2 + y^2 = 10
x + y = 0

Answer

x - y = 10
y = 10 - x

Question 62

Solve the equation: 2x + 5 = 13

Accepted Answer

x = 4

Answer

x = 5

Answer

x = 6

Answer

x = 7