Algebra

Algebra is the part of mathematics where we use letters to stand in for numbers. Once you can do that, you can write rules that work for ANY number — which is how everything from M-Pesa fees to building plans to scientific formulas is calculated.

Variables and constants:

• A variable is a letter that stands for a number whose value can change. The most common letters are x, y, n. In x + 5 = 12, the variable x can be solved to find its value (here, 7).
• A constant is a fixed number. In 2x + 3, the 3 is a constant; x is the variable.
• A coefficient is the number multiplying a variable. In 2x, the 2 is the coefficient. If you just write x, the coefficient is understood to be 1.

Algebraic expressions:

An expression is a combination of numbers, variables and operations — but with NO equals sign. Examples: 3x + 5, 2a − b, x² + 4x − 7. You cannot "solve" an expression; you can only simplify it.

Algebraic equations:

An equation has an equals sign. The left side equals the right side. Examples: x + 7 = 10, 3y = 21, 2x − 1 = 9. The job in an equation is to find the value(s) of the variable that make the two sides equal.

Like terms:

Terms with the SAME variable raised to the SAME power are like terms and can be added or subtracted. 3x and 5x are like terms (sum: 8x). 3x and 5x² are NOT like terms — different powers. 3x and 5y are NOT like terms — different variables.

Solving equations using the balance method:

Think of an equation as a balance scale. Whatever you do to one side, you MUST do to the other. Steps:

1. Get the variable on one side; numbers on the other.
2. Add or subtract the same number from BOTH sides to move terms.
3. Multiply or divide BOTH sides by the same number to isolate the variable.
4. Write the answer.

Substitution:

If you know the value of a variable, you can substitute it into an expression to evaluate. If x = 4, then 2x + 3 = 2(4) + 3 = 8 + 3 = 11.

Common mistakes to avoid:

• Treating x and 2x as the same thing. 2x means "2 times x", not "the number 2x".
• Forgetting to apply an operation to BOTH sides of an equation. Whatever you subtract from the left, you must subtract from the right.
• Combining unlike terms. 3x + 5y cannot be simplified — they're different variables.
• Sign errors when moving terms across the equals sign. x + 5 = 12 becomes x = 12 − 5, not x = 12 + 5.
• Dividing only part of one side. In 2x + 4 = 10, you can subtract 4 first (then divide by 2); you cannot just divide by 2 because the 4 isn't being multiplied.

CBC Grade 4 introduces using letters to represent numbers; Grade 5–6 covers simple equations and patterns; Grade 7 introduces algebraic expressions, like terms, linear equations and inequalities; Grade 8 extends to factorising and simultaneous equations; Grade 9 covers matrices, straight-line equations and graphical solutions — the foundation for KJSEA and senior school Mathematics.