---
title: "Solving linear equations"
description: "Use algebraic methods to solve linear equations in one variable, including rearranging, expanding brackets, collecting terms on both sides, and working with rational coefficients."
canonical: https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO
source: https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO.md
retrieved: 2026-10-19
---

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# Solving linear equations

Use algebraic methods to solve linear equations in one variable, including rearranging, expanding brackets, collecting terms on both sides, and working with rational coefficients.

Subject: Mathematics · Area: Algebra · Ages 11 to 14
Page: https://lightmysky.com/learn/mathematics/solving-linear-equations-mt_QhFEDyIwSO

## Ready when they can

- Solve one-step and two-step linear equations in one variable
- Solve equations requiring expansion of brackets and collection of like terms
- Solve equations with the unknown on both sides and with fractional or negative coefficients

## Lesson: Solving for x

An equation is like a balance. Both sides always stay equal. Your job is to get x alone on one side, using inverse operations to undo whatever has been done to it.

*(drawing: First undo the plus 7, then undo the times 3. Whatever you do to one side, do the same to the other.)*

**Example.** To solve 3(x + 2) = 21, expand the bracket first: 3x + 6 = 21. Subtract 6 from both sides: 3x = 15. Divide by 3: x = 5.

**Example.** When x is on both sides, like 5x - 4 = 2x + 8, move the x terms together first. Subtract 2x from both sides: 3x - 4 = 8. Add 4: 3x = 12. Divide by 3: x = 4.

**Tip.** A negative or fractional coefficient does not change the plan. Divide or multiply both sides by the coefficient of x, whether it is negative or fractional.

**Recap.** Whatever operation you use, apply it to both sides, until x stands alone.

## Practice

20 questions on this page, each with its working shown.

## Needs first

- [Expanding Single Brackets](https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN)
- [Writing Algebraic Equations](https://lightmysky.com/learn/mathematics/writing-algebraic-equations-mt_i9rJbuFO3p)
- [Sign Rules for Multiplication and Division](https://lightmysky.com/learn/mathematics/sign-rules-for-multiplication-and-division-mt_rxInpOQ74w)
- [Substituting into Formulae](https://lightmysky.com/learn/mathematics/substituting-into-formulae-mt_vHzVa3SURC)
- [Using inverse operations](https://lightmysky.com/learn/mathematics/using-inverse-operations-mt_VUQNveSYjQ)

## Opens up

- [Simple formulae](https://lightmysky.com/learn/mathematics/simple-formulae-mt_3qrCtdoVAU)
- [Nth-Term Rules](https://lightmysky.com/learn/mathematics/nth-term-rules-mt_HRKzwEQJgO)
- [Inequalities and their solution sets](https://lightmysky.com/learn/mathematics/inequalities-and-their-solution-sets-mt_i2F1nWxJjv)
- [Simultaneous equations](https://lightmysky.com/learn/mathematics/simultaneous-equations-mt_mqgu72aCMz)