Algebra · Quick Reference

Linear Equations Cheat Sheet

Algebra I · Lesson 1/17

In one line: a linear equation states that two expressions are equal, with variables appearing only to the first power — solving one means finding the value that makes both sides balance.

Key Ideas

1What Makes an Equation Linear. Every variable term has an exponent of exactly 1 (no x^2, sqrt(x), or 1/x terms) — its graph is always a straight line.

2The Balance Principle. Whatever operation you do to one side of an equation, you must do to the other side too, to keep both sides equal.

3Solving Multi-Step Equations. Use inverse operations in reverse order of PEMDAS: undo addition/subtraction first, then multiplication/division, isolating the variable last.

4Variables on Both Sides. Move all variable terms to one side and all constants to the other by adding or subtracting the same term from both sides.

5Checking Solutions. Substitute your answer back into the original equation; both sides should come out equal.

Worked Examples

Solve for x: 3x + 5 = 20.

x = 5

Solve for x: 2x + 7 = x + 15.

x = 8

Solve for x: 4(x - 2) = 16.

x = 6

Formulas

If a = b, then a+c = b+c, a-c = b-c, a*c = b*c, and a/c = b/c (c not 0)

Practice Yourself

Solve for x: 2x + 3 = 11.

x = 4

Solve for x: 5x - 4 = 16.

x = 4

Solve for x: 3x + 2 = x + 10.

x = 4