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Maths Quiz - Level 5-6 Algebra - Equations - Basic (Questions)

Solve basic linear equations in KS3 algebra. Use inverse operations to isolate the variable and check solutions by substitution with clear, step by step working.

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Fascinating Fact:

In shopping, if three apples cost £1.50, the equation 3x = 1.50 helps find the price of one apple, x = 0.50.

In KS3 Maths, basic equations model real situations and help you find unknown values. You will use the balance method, apply inverse operations in the correct order, keep both sides equal, and check answers by substituting back.

Key Terms

Equation: A statement showing two expressions are equal, often containing an unknown.
Variable: The letter that stands for an unknown number, for example x or y.
Inverse operation: An operation that undoes another, such as subtract undoing add, or divide undoing multiply.

Frequently Asked Questions (Click to see answers)

How do I solve a simple linear equation step by step?

Use inverse operations on both sides. Example: 3x + 5 = 20. Subtract 5 to get 3x = 15, then divide by 3 to get x = 5.

What is the balance method in equations?

The balance method means doing the same operation to both sides so equality stays true. Treat the equals sign like a balance that must stay level.

How can I check if my solution to an equation is correct?

Substitute the value back into the original equation. If both sides give the same number, your solution is correct. Example: for x = 5, 3(5) + 5 = 20.

Try These Related Quizzes

1.

An equation must have two equal what?

[ ]	Examples
[ ]	Expressions
[ ]	Extensions
[ ]	Extractions

2.

What is the name give to an equation that doesn't balance on either side of the equals sign?

[ ]	Inaccurate
[ ]	Inept
[ ]	Invalid
[ ]	There is no such thing

3.

If you are given an equation, what will you have done to it when you have found the answers?

[ ]	Soaked it
[ ]	Solved it
[ ]	Squared it
[ ]	Stuffed it

4.

If x + 4 = b, what is the value of x?

[ ]	4b
[ ]	-4b
[ ]	b + 4
[ ]	b - 4

5.

Which of these is not an equation?

[ ]	6/3 = 2
[ ]	65 + 35 = 100
[ ]	5 - 6 = 8 - 9
[ ]	2 x 3 = 7 - 2

6.

If 4 + x + 8 = 24, then which of the following is correct?

[ ]	4 + x = 16
[ ]	12 + x = 16
[ ]	4x - 8 = 16
[ ]	4x + 8 =16

7.

If 9x - 2 = 7, then which of the following is not correct?

[ ]	9x = 7 + 2
[ ]	9x = 9
[ ]	x = ⁹⁄₉
[ ]	x = 2

8.

If a = 5 and b = 8, then which of the following is correct?

[ ]	8 + a + 8 + b = 104
[ ]	8 + a + 8b = 104
[ ]	8a + 8 + b = 104
[ ]	8a + 8b = 104

9.

If 3a + 2 = a + 6, then which of these is incorrect?

[ ]	3a + 2 - a = 6
[ ]	2a = 6 + 2
[ ]	2a = 4
[ ]	a = ⁴⁄₂

10.

Which of the following numbers is a possible value for x in the equation x³ = x² + 18?

[ ]	2
[ ]	3
[ ]	4
[ ]	5

You can find more about this topic by visiting BBC Bitesize - Equations

Maths Quiz - Level 5-6 Algebra - Equations - Basic (Answers)

1.

An equation must have two equal what?

[ ]	Examples
[x]	Expressions
[ ]	Extensions
[ ]	Extractions

You must have one expression on one side of the equals sign and another expression on the other side. The two sides must share the same value. If one side equals 56 then the other side must also equal 56

2.

What is the name give to an equation that doesn't balance on either side of the equals sign?

[ ]	Inaccurate
[ ]	Inept
[ ]	Invalid
[x]	There is no such thing

Either the expressions balance and it is an equation or the expressions don't balance and it isn't an equation!

3.

If you are given an equation, what will you have done to it when you have found the answers?

[ ]	Soaked it
[x]	Solved it
[ ]	Squared it
[ ]	Stuffed it

A 'solution' is what you are looking for when trying to solve an equation

4.

If x + 4 = b, what is the value of x?

[ ]	4b
[ ]	-4b
[ ]	b + 4
[x]	b - 4

When + 4 crosses over to the other side of the equals sign it must be changed to - 4

5.

Which of these is not an equation?

[ ]	6/3 = 2
[ ]	65 + 35 = 100
[ ]	5 - 6 = 8 - 9
[x]	2 x 3 = 7 - 2

In the correct answer, the expressions on either side of the equals sign are not the same value and therefore it is not an equation

6.

If 4 + x + 8 = 24, then which of the following is correct?

[x]	4 + x = 16
[ ]	12 + x = 16
[ ]	4x - 8 = 16
[ ]	4x + 8 =16

You must firstly have ascertained that x = 12

7.

If 9x - 2 = 7, then which of the following is not correct?

[ ]	9x = 7 + 2
[ ]	9x = 9
[ ]	x = ⁹⁄₉
[x]	x = 2

Everything was going fine until the last item! To be correct, the last item would need to be x = 1

8.

If a = 5 and b = 8, then which of the following is correct?

[ ]	8 + a + 8 + b = 104
[ ]	8 + a + 8b = 104
[ ]	8a + 8 + b = 104
[x]	8a + 8b = 104

(8 x 5) + (8 x 8) = 40 + 64 = 104

9.

If 3a + 2 = a + 6, then which of these is incorrect?

[ ]	3a + 2 - a = 6
[x]	2a = 6 + 2
[ ]	2a = 4
[ ]	a = ⁴⁄₂

To correct the equation it should read 2a = 6 - 2. All of the above leads us to the conclusion that a = 2

10.

Which of the following numbers is a possible value for x in the equation x³ = x² + 18?

[ ]	2
[x]	3
[ ]	4
[ ]	5

You can work this one out by trial and error. 2³ = 8 so is too low. 4³ = 64 so is too high. Therefore the answer must be between 2 and 4 so it hast to be 3