Algebra Basics Math · Noduly
Lesson

Letters that stand for numbers

Algebra is just arithmetic with placeholders. A variable like x stands in for a number you don't yet know — and an equation tells you what's true about it.

Variables and constants

A variable is a symbol (often x or y) that holds a number. A constant is a fixed number. In 3x + 7, x is the variable, 3 is the coefficient, 7 is the constant.

Equations

An equation says two expressions are equal. To solve, do the same thing to both sides until the variable stands alone. x + 5 = 12 → x = 7.

Inequalities

Use <, >, ≤, ≥. Solve like equations — but if you multiply or divide by a negative, flip the inequality: −2x > 6 → x < −3.

Functions and graphs

A function takes an input and produces one output. The graph of y = mx + b is a straight line — slope m, y-intercept b.

Headline rules

Order of operations
PEMDAS / BODMAS
Distributive
a(b + c) = ab + ac
Slope
m = (y₂ − y₁)/(x₂ − x₁)
Slope-intercept
y = mx + b
Point-slope
y − y₁ = m(x − x₁)
Standard form
Ax + By = C
Function
f(x) = output
Inequality flip
×(−1) flips < ↔ >

Hands-on tools

Solve on a balance, slide a line, or translate a story into algebra.

Balance scale solver

Whatever you do to one side, do to the other. Click an operation to apply.

2x + 3 = 11

Slope-intercept playground

Drag the sliders. The line and equation update together.

y = 2x + 1

Inequality grapher

Pick a comparison and a value. Open dot for strict, closed dot for ≤ or ≥.

x

x < 3 — every x to the left of 3 (open dot, value 3 not included).

Word problem translator

Highlighted phrases map to algebra. Click a phrase for a hint.

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Quiz

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Flashcards

Tap a card to flip. ← / → keys to navigate.

Variable
VariableSymbol (often x or y) that stands for an unknown number.
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For teachers

Print-ready worksheet, answer key, teaching tips and standards alignment.

Teaching tips

    Standards alignment

      Reference

      Formula sheet

      Slope
      m = (y₂ − y₁)/(x₂ − x₁)
      Slope-intercept
      y = mx + b
      Point-slope
      y − y₁ = m(x − x₁)
      Standard form
      Ax + By = C
      Distance (1D)
      |a − b|
      Distributive
      a(b + c) = ab + ac
      FOIL
      (a+b)(c+d) = ac+ad+bc+bd
      Quadratic formula
      x = (−b ± √(b²−4ac)) / 2a
      Function notation
      f(x) = mx + b
      Inequality flip
      × or ÷ negative ⇒ flip sign

      Photo gallery

      Images sourced from Wikipedia.

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