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Updated 25 Feb 2026

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5 pages

Mastering Linear Equations: Solve Like a Pro

Solving equations is like being a detective - you're hunting... Show more

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# Solving Equations

## What it's all about

Solving an equation is like being a detective. We have to find the value of a
mystery number, w

What's All This About?

Solving equations means finding the value of an unknown number, called a variable. Your main mission is simple: get that variable all by itself on one side of the equals sign.

An equation is just a maths sentence saying two things are equal - it always has that equals sign in the middle. The variable is the mystery letter (like x or y) you need to find, while constants are just regular numbers hanging about.

Here's your secret weapon: inverse operations. These are opposite operations that undo each other - addition undoes subtraction, multiplication undoes division, and so on.

Remember: Addition ↔ Subtraction and Multiplication ↔ Division are perfect pairs!

Cracking One-Step Equations

These are the easiest equations because they only need one inverse operation to solve. You've basically got two types to deal with.

For addition and subtraction equations, spot what number is being added or subtracted from your variable. Then do the opposite to both sides. If you see x + 6 = 14, subtract 6 from both sides to get x = 8.

For multiplication and division equations, look at what number your variable is being multiplied or divided by. Then do the reverse to both sides. If you have 4y = 20, divide both sides by 4 to get y = 5.

Top Tip: Always do the same operation to both sides - this keeps your equation balanced like a perfect seesaw!

Tackling Two-Step Equations

Two-step equations need two moves to solve, and here's the clever bit - you work backwards through BIDMAS. Think of it like unwrapping a present where you undo the last thing that was done first.

Step 1: Deal with any addition or subtraction first. Get rid of the constant (the number on its own) by doing the opposite operation to both sides.

Step 2: Then handle any multiplication or division. Work on the number attached to your variable by using its inverse operation.

For example, with 2x + 5 = 15, first subtract 5 from both sides $giving 2x = 10$ , then divide both sides by 2 $giving x = 5$ .

Golden Rule: Always tackle the lone number first, then deal with whatever's attached to your variable!

Working Through Real Examples

Let's see how this works with proper exam-style examples. For a simple equation like a - 9 = 11, you add 9 to both sides to get a = 20.

With two-step equations like 3m + 4 = 19, first subtract 4 from both sides $3m = 15$ , then divide both sides by 3 $m = 5$ . Easy when you know the steps!

Even trickier ones like k/5 - 2 = 3 follow the same pattern. Add 2 to both sides first $k/5 = 5$ , then multiply both sides by 5 $k = 25$ .

Always check your answer by popping it back into the original equation. It takes seconds and can save you marks in a test!

Pro Move: Checking your answer is like having a safety net - it catches mistakes before they cost you points!

Key Things to Remember

The golden rule of algebra is sacred: whatever you do to one side, you absolutely must do to the other. No exceptions, ever!

Watch out for negative numbers - if you have -3x = 12, you divide by -3 (not just 3) to get x = -4. Also remember that x on its own is really 1x, and x/2 just means x ÷ 2.

For two-step equations, your order of attack is: undo addition or subtraction first, then tackle multiplication or division. Keep everything balanced and always check your final answer.

Test Strategy: Goal → Get the variable alone. Method → Use inverse operations. Rule → Do the same to both sides. Check → Put your answer back in!

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Mathematics

•

Updated 25 Feb 2026

•

5 pages

Mastering Linear Equations: Solve Like a Pro

Solving equations is like being a detective - you're hunting for the mystery value of a variable (usually x or y). Think of an equation as a perfectly balanced weighing scale, where whatever you do to one side, you must... Show more

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What's All This About?

Solving equations means finding the value of an unknown number, called a variable. Your main mission is simple: get that variable all by itself on one side of the equals sign.

Here's your secret weapon: inverse operations. These are opposite operations that undo each other - addition undoes subtraction, multiplication undoes division, and so on.

Remember: Addition ↔ Subtraction and Multiplication ↔ Division are perfect pairs!

Sign up to see the contentIt's free!

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Improve your grades

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Cracking One-Step Equations

These are the easiest equations because they only need one inverse operation to solve. You've basically got two types to deal with.

Top Tip: Always do the same operation to both sides - this keeps your equation balanced like a perfect seesaw!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

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Tackling Two-Step Equations

Two-step equations need two moves to solve, and here's the clever bit - you work backwards through BIDMAS. Think of it like unwrapping a present where you undo the last thing that was done first.

Step 1: Deal with any addition or subtraction first. Get rid of the constant (the number on its own) by doing the opposite operation to both sides.

Step 2: Then handle any multiplication or division. Work on the number attached to your variable by using its inverse operation.

For example, with 2x + 5 = 15, first subtract 5 from both sides $giving 2x = 10$ , then divide both sides by 2 $giving x = 5$ .

Golden Rule: Always tackle the lone number first, then deal with whatever's attached to your variable!

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Working Through Real Examples

Let's see how this works with proper exam-style examples. For a simple equation like a - 9 = 11, you add 9 to both sides to get a = 20.

With two-step equations like 3m + 4 = 19, first subtract 4 from both sides $3m = 15$ , then divide both sides by 3 $m = 5$ . Easy when you know the steps!

Even trickier ones like k/5 - 2 = 3 follow the same pattern. Add 2 to both sides first $k/5 = 5$ , then multiply both sides by 5 $k = 25$ .

Always check your answer by popping it back into the original equation. It takes seconds and can save you marks in a test!

Pro Move: Checking your answer is like having a safety net - it catches mistakes before they cost you points!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Key Things to Remember

The golden rule of algebra is sacred: whatever you do to one side, you absolutely must do to the other. No exceptions, ever!

Watch out for negative numbers - if you have -3x = 12, you divide by -3 (not just 3) to get x = -4. Also remember that x on its own is really 1x, and x/2 just means x ÷ 2.

For two-step equations, your order of attack is: undo addition or subtraction first, then tackle multiplication or division. Keep everything balanced and always check your final answer.

Test Strategy: Goal → Get the variable alone. Method → Use inverse operations. Rule → Do the same to both sides. Check → Put your answer back in!