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Linear Equations (Numerical) (F)

Solve GCSE Foundation linear equations. Balance both sides, clear fractions, and combine like terms to find x. Practise one-step, two-step, and equations with brackets.

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Fascinating Fact:

In sports stats, x⁄3 + x = 8. Multiply everything by 3 to get x + 3x = 24, so 4x = 24 and x = 6. Clear denominators first.

In GCSE Maths (Foundation), numerical linear equations are solved by keeping both sides balanced. You’ll clear fractions, expand brackets, combine like terms, and use inverse operations to isolate the unknown.

Key Terms

Coefficient: The number multiplying a variable, e.g., 5 in 5x.
Like terms: Terms with the same variable and power, which can be combined (e.g., 2x + 3x = 5x).
Inverse operation: An operation that “undoes” another, like +3 and −3, or ×4 and ÷4.

Frequently Asked Questions (Click to see answers)

How do you solve linear equations with fractions?

Multiply every term by the lowest common multiple of the denominators to clear fractions, then simplify and isolate the variable using inverse operations.

What does “balance both sides” mean in algebra?

Whatever you do to one side of the equation, you must do to the other side as well. This keeps the equality true while you rearrange.

How do I check my solution to an equation?

Substitute your value back into the original equation. If both sides are equal after simplifying, your solution is correct.