Linear equations quiz: 25 questions with answers

Questions and answers

By CanQuiz

An AI wrote the questions in this quiz from its creator’s material. It may contain mistakes.

1. 1.Solve 3x + 5 = 20.

   • x = 5
   • x = 25/3
   • x = 15
   • x = 3
   Show answer

   Answer: x = 5

   Explanation: Subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. Check: 3 · 5 + 5 = 20.

2. 2.Solve 2(x − 4) = 10.

   • x = 9
   • x = 7
   • x = 1
   • x = 14
   Show answer

   Answer: x = 9

   Explanation: Expanding the bracket gives 2x − 8 = 10, so 2x = 18 and x = 9. The answer 7 comes from multiplying only the x by 2 and forgetting the −4.

3. 3.Which of these is a linear equation in one unknown?

   • 4x − 7 = 2x + 1
   • x² + 3 = 12
   • 1/x = 5
   • √x = 4
   Show answer

   Answer: 4x − 7 = 2x + 1

   Explanation: In a linear equation the unknown appears only to the first power, not squared, under a root or in a denominator. Only 4x − 7 = 2x + 1 meets that condition.

4. 4.x = −2 is a solution of 5x + 3 = −7.

   • True
   • False
   Show answer

   Answer: True

   Explanation: Substituting gives 5 · (−2) + 3 = −10 + 3 = −7, which equals the right-hand side, so x = −2 is a solution.

5. 5.Solve x/4 − 3 = 2.

   • x = 20
   • x = −4
   • x = 4
   • x = 5/4
   Show answer

   Answer: x = 20

   Explanation: Add 3 to both sides to get x/4 = 5, then multiply both sides by 4 to get x = 20.

6. 6.Which step turns 7x = 42 into an equivalent equation that gives the value of x directly?

   • Divide both sides by 7
   • Subtract 7 from both sides
   • Multiply both sides by 7
   • Divide only the left side by 7
   Show answer

   Answer: Divide both sides by 7

   Explanation: Dividing both sides by the coefficient 7 leaves x alone and gives x = 6. Changing only one side would break the balance of the equation.

7. 7.Solve 5x − 3 = 2x + 9.

   • x = 4
   • x = 2
   • x = 12
   • x = −4
   Show answer

   Answer: x = 4

   Explanation: Subtract 2x from both sides and add 3 to both sides to get 3x = 12, so x = 4.

8. 8.Multiplying both sides of an equation by 0 gives an equivalent equation.

   • True
   • False
   Show answer

   Answer: False

   Explanation: Multiplying by 0 turns any equation into 0 = 0, which is true for every value, so the original solution is lost. Only multiplying or dividing by a non-zero number keeps the equation equivalent.

9. 9.Solve 3(2x + 1) − 4x = 15.

   • x = 6
   • x = 4
   • x = 3
   • x = 9
   Show answer

   Answer: x = 6

   Explanation: Expanding gives 6x + 3 − 4x = 15, which simplifies to 2x + 3 = 15. Then 2x = 12 and x = 6.

10. 10.Solve (x + 2)/3 = (x − 1)/2.

    • x = 7
    • x = −7
    • x = 1
    • x = 5
    Show answer

    Answer: x = 7

    Explanation: Multiplying both sides by 6 gives 2(x + 2) = 3(x − 1), so 2x + 4 = 3x − 3. Moving the terms gives x = 7.

11. 11.How many solutions does the equation 2(x + 3) = 2x + 6 have?

    • Exactly one
    • None
    • Infinitely many
    • Exactly two
    Show answer

    Answer: Infinitely many

    Explanation: Expanding the left side gives 2x + 6, the same expression as the right side. The equation is an identity, so every number is a solution.

12. 12.How many solutions does the equation 4x − 1 = 4x + 5 have?

    • Exactly one
    • None
    • Infinitely many
    • Exactly two
    Show answer

    Answer: None

    Explanation: Subtracting 4x from both sides leaves −1 = 5, which is false. No value of x can make the two sides equal.

13. 13.A number is doubled and then increased by 7, and the result is 31. What is the number?

    • 12
    • 19
    • 24
    • 7
    Show answer

    Answer: 12

    Explanation: Calling the number n gives 2n + 7 = 31, so 2n = 24 and n = 12.

14. 14.The sum of three consecutive integers is 72. What is the smallest of them?

    • 23
    • 24
    • 22
    • 25
    Show answer

    Answer: 23

    Explanation: Writing the integers as n, n + 1 and n + 2 gives 3n + 3 = 72, so 3n = 69 and n = 23. The three numbers are 23, 24 and 25.

15. 15.A taxi charges $3 to start a ride plus $2 for every km driven. One ride cost $19 in total. How many km was the ride?

    • 8 km
    • 9.5 km
    • 11 km
    • 6 km
    Show answer

    Answer: 8 km

    Explanation: With k the number of km, the total cost is 3 + 2k, so 3 + 2k = 19. Then 2k = 16 and k = 8, so the ride was 8 km.

16. 16.Solve 0.5x + 1.5 = 4.

    • x = 5
    • x = 11
    • x = 2.5
    • x = 1.25
    Show answer

    Answer: x = 5

    Explanation: Subtract 1.5 to get 0.5x = 2.5, then divide by 0.5 (or multiply by 2) to get x = 5.

17. 17.The equations 3x = 12 and x + 5 = 9 are equivalent.

    • True
    • False
    Show answer

    Answer: True

    Explanation: Equivalent equations have the same solutions. Both have the single solution x = 4.

18. 18.Solve −3x + 7 = 1.

    • x = 2
    • x = −2
    • x = 8/3
    • x = −8/3
    Show answer

    Answer: x = 2

    Explanation: Subtract 7 from both sides to get −3x = −6. Dividing by −3 gives x = 2, since a negative divided by a negative is positive.

19. 19.Solve x/2 + x/3 = 10.

    • x = 12
    • x = 50
    • x = 2
    • x = 6
    Show answer

    Answer: x = 12

    Explanation: Multiplying every term by 6 clears the fractions: 3x + 2x = 60, so 5x = 60 and x = 12. The answer 50 comes from wrongly adding the denominators to get x/5.

20. 20.What is the correct way to check a solution of an equation?

    • Substitute the value into the original equation and see whether both sides are equal
    • Solve the equation a second time using exactly the same steps
    • Substitute the value only into the last line of your working
    • Check that the value is a whole number
    Show answer

    Answer: Substitute the value into the original equation and see whether both sides are equal

    Explanation: A mistake made early in the working carries into every later line, so only the original equation gives a fair check. If both sides give the same number, the value is a solution.

21. 21.For which value of a does the equation ax + 4 = 10 have the solution x = 3?

    • a = 2
    • a = 3
    • a = 6
    • a = 14/3
    Show answer

    Answer: a = 2

    Explanation: Putting x = 3 into the equation gives 3a + 4 = 10, so 3a = 6 and a = 2.

22. 22.The solution of 6 − 2x = 0 is x = −3.

    • True
    • False
    Show answer

    Answer: False

    Explanation: Adding 2x to both sides gives 6 = 2x, so x = 3. Checking x = −3 gives 6 + 6 = 12, not 0.

23. 23.A mother is 4 times as old as her son. In 20 years she will be twice as old as he is. How old is the son now?

    • 10
    • 20
    • 5
    • 40
    Show answer

    Answer: 10

    Explanation: With the son's age s, the mother is 4s, and in 20 years 4s + 20 = 2(s + 20). That gives 4s + 20 = 2s + 40, so 2s = 20 and s = 10.

24. 24.A rectangle is 5 cm longer than it is wide, and its perimeter is 38 cm. What is its width?

    • 7 cm
    • 12 cm
    • 8.25 cm
    • 16.5 cm
    Show answer

    Answer: 7 cm

    Explanation: With width w, the length is w + 5 and the perimeter is 2(w + w + 5) = 4w + 10. From 4w + 10 = 38 we get 4w = 28 and w = 7 cm.

25. 25.Adding the same number to both sides of an equation does not change its solution.

    • True
    • False
    Show answer

    Answer: True

    Explanation: Adding the same amount to both sides keeps them equal, so the new equation is equivalent to the old one. This is the rule used to move a term from one side to the other.