Basic Algebra: Symbols That Stand for Numbers

Letters as boxes for numbers

Algebra begins with a small idea: let a letter hold a number you do not know yet. Then write rules that stay true no matter which number fills the box—until a specific problem pins it down.

Equations as balances

An equation is a balance scale. Whatever you do to one side, do to the other:

x + 3 = 7

Subtract 3 from both sides:

x = 4

The unknown becomes known because the balance never tipped.

Expressions vs equations

An expression is a recipe, like 2x + 5. An equation asserts two recipes are equal. Solving means finding values that make the assertion true.

Combining like terms

Terms with the same variable power can merge:

3x + 5x - 2 = 8x - 2

Clearer form, same value for every x.

Distributing

Multiplication spreads across a sum:

2(x + 4) = 2x + 8

This is the reverse of factoring—two views of the same quantity.

A tiny system

Two unknowns need two relationships:

x + y = 10
x - y = 2

Add the equations: 2x = 12, so x = 6, then y = 4. Structure, not guessing, unlocks the pair.

Takeaway

Algebra is careful bookkeeping with placeholders. Keep both sides honest, collect like terms, and the unknown has nowhere left to hide.