Simple Equations: quick revision, 15 bites

An Equation Is a Balanced Scale

Both sides must always stay equal.

A simple equation says two expressions are **equal**. Whatever you do to one side, you must do to the other — just like keeping a balance scale level.

Takeaway. Treat an equation like a balance: every operation must be mirrored on both sides.

Key Terms You Must Know

Speak the language of equations.

Takeaway. Every equation has a variable, two sides, and a solution that balances them.

The General Form of a Simple Equation

One pattern covers them all.

Solving means finding $x$ such that the equation holds. For example, $2x + 3 = 11$ gives $x = 4$.

Takeaway. Most simple equations reduce to the form $ax + b = c$.

Solve Any Simple Equation in 3 Steps

Isolate, simplify, verify.

Takeaway. Undo operations in reverse order, then always verify by substitution.

Don't Change Only One Side

One-sided changes break the balance.

Takeaway. Every operation must be mirrored on both sides — no exceptions.

Sign Errors When Transposing

Flip the sign when you cross over.

Takeaway. Transposing a term across '=' reverses its sign.

Worked Example: Variable on Both Sides

Bring variables together first.

Takeaway. Collect all variable terms on one side, constants on the other.

Equations Solve Everyday Problems

From bills to budgets, equations rule.

Takeaway. Any 'find the unknown' real-life problem often becomes a simple equation.

Remember: Opposite Operations Undo

Addition undoes subtraction — always.

Takeaway. Use the inverse operation to peel away everything around the variable.

Score Full Marks: Show Every Step

Steps earn marks, not just answers.

Takeaway. Examiners award method marks — never skip the working.

Expression vs Equation

One has '=', the other doesn't.

Takeaway. An equation is two expressions joined by '='; an expression alone cannot be 'solved'.

A Simple Equation Has Exactly One Solution

One variable, one answer.

A linear equation in one variable ($ax + b = c$, $a \neq 0$) has **exactly one solution** — the value that makes both sides equal.

Takeaway. Degree-1 equations in one variable always have a unique solution.

Setting Up an Equation from a Word Problem

Translate words into math.

Takeaway. Word problems become easy once you translate them into an equation.

Don't Forget to Divide by the Coefficient

The number in front matters.

Takeaway. Always divide by the coefficient to fully isolate the variable.

The Word 'Algebra' Comes from Arabic

A 1,200-year-old math tradition.

The word *algebra* comes from **al-jabr**, a term used by the 9th-century mathematician **Al-Khwarizmi** in his book on solving equations.

Takeaway. Equation-solving is one of the oldest tools in mathematics.