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Pre-Algebra & Algebra Basics

Algebra is just arithmetic with a letter standing in for a number you don't know yet. Master a few rules and you can solve for almost anything.

Order of operations (PEMDAS)

When an expression has several steps, you must do them in the right order, or you'll get the wrong answer:

2 + 3 × 4 = 2 + 12 = 14 (not 20 — multiply before you add)

Negative numbers

The rules that trip people up the most:

−3 + (−5) = −8  (same signs: add, keep the sign)
−7 + 4 = −3  (different signs: subtract, keep the bigger sign)
−4 × −6 = +24  (two negatives multiply to a positive)

Variables and expressions

A variable is a letter that holds a number you don't know yet — usually x. An expression mixes numbers and variables, like 3x + 5. 3x means "3 times x".

Combining like terms

You can only add or subtract terms that have the same variable. Think of it as counting: 3 apples + 2 apples = 5 apples.

3x + 2x + 5 − 1 = 5x + 4

The distributive property

A number outside parentheses multiplies everything inside:

3(x + 4) = 3·x + 3·4 = 3x + 12

Solving equations

The golden rule: whatever you do to one side, do to the other. Your goal is to get the variable alone on one side.

One step — undo the +5 by subtracting 5:

x + 5 = 12

x + 5 − 5 = 12 − 5

x = 7

Two steps — subtract first, then divide:

2x + 3 = 11

2x = 11 − 3 = 8

x = 8 ÷ 2

x = 4

Check your answer by plugging it back in: 2(4) + 3 = 8 + 3 = 11 ✓

Shaky on fractions first?

Fractions show up all over algebra. Brush them up before you dive in.

Review fractions →