What is a linear equation in one variable?

It is an equation with only one variable (like x) whose highest power is 1, for example 2x + 3 = 11. Solving it means finding the single value of the variable that makes both sides equal.

How do you solve a linear equation step by step?

Move all the variable terms to one side and the numbers to the other, remembering that a term changes its sign when it crosses the equals sign. Simplify both sides, then divide by the number multiplying the variable. Finally, put your answer back into the original equation to check it.

What does 'transposing' mean in maths?

Transposing means moving a term from one side of the equals sign to the other. When a term moves across, its operation reverses: a plus becomes a minus, and something that was multiplying becomes dividing. It is a shortcut for doing the same operation to both sides.

Class 8 Maths: Linear Equations in One Variable — Explained Simply

A linear equation in one variable is just a number sentence with one unknown, where the unknown's power is 1. Something like 2x + 3 = 11. The two sides of the = sign are like a balanced scale: whatever you do to one side, you must do to the other to keep it balanced. Solving means finding the value of x that keeps both sides equal.

The one rule: keep the balance

You can add, subtract, multiply or divide — as long as you do the same thing to both sides. To solve 2x + 3 = 11: subtract 3 from both sides (2x = 8), then divide both sides by 2 (x = 4). That's the whole idea.

Transposing — the handy shortcut

Doing the same thing to both sides every time is slow, so we use transposing: move a term across the equals sign and flip its operation.

✓ A + term becomes a − term when it crosses: x + 5 = 9 → x = 9 − 5 = 4.
✓ A term that multiplies becomes one that divides: 3x = 12 → x = 12 ÷ 3 = 4.

Variables on both sides

When x appears on both sides, gather the x-terms on one side and the numbers on the other. Solve 4x − 3 = x + 6: transpose x to the left and −3 to the right → 4x − x = 6 + 3 → 3x = 9 → x = 3.

Equations with brackets and fractions

First open any brackets, then clear fractions by multiplying every term by the common denominator. For 2(x + 1) = 10: open the bracket → 2x + 2 = 10 → 2x = 8 → x = 4. Always tidy the equation before you transpose.

Word problems — turn words into an equation

Let the unknown be x, write the sentence as an equation, then solve. "A number increased by 7 gives 20." → x + 7 = 20 → x = 13. The trick is naming the unknown clearly, then translating each phrase into maths one piece at a time.

Always check your answer

Put your value back into the original equation. For x = 4 in 2x + 3 = 11: 2(4) + 3 = 11 ✓. If both sides match, you're correct — a habit that catches almost every silly mistake.

Want this taught step by step?

Equations click much faster when each move is shown and your child solves one themselves. Upload the chapter to Tutorfic and it works through examples one step at a time, in your child's language, then sets a short quiz with the reasoning behind every answer. It's one of all the Class 8 subjects Tutorfic teaches.

Class 8 Maths: Linear equations in one variable