Chapter 02 of 10

Equations

How do you isolate an unknown without changing the truth of an equation?

An equation says two expressions have the same value. Solving means finding every value that makes that statement true. The central rule is balance: whatever operation you perform on one side must also be performed on the other.

01

The big ideas

Understand these before you worry about speed.

Use inverse operations

Undo addition with subtraction, multiplication with division, and so on. Work in reverse order to isolate the variable.

Example3x + 4 = 19 → 3x = 15 → x = 5.

Simplify before isolating

Distribute and combine like terms on each side before moving variable terms and constants.

Example2(x + 3) = 14 becomes 2x + 6 = 14, then x = 4.

Recognize special results

A true statement such as 0 = 0 means infinitely many solutions. A false one such as 0 = 5 means no solution.

Example2(x + 1) = 2x + 2 is true for every real x.
02

Worked example

Follow the reason for each step—not just the symbols.

Problem

Solve 4(2x − 1) = 3x + 21.

  1. Distribute: 8x − 4 = 3x + 21.
  2. Subtract 3x from both sides: 5x − 4 = 21.
  3. Add 4: 5x = 25.
  4. Divide by 5: x = 5.
Answerx = 5
03

Try it yourself

Work on paper first. Open each answer only when you are ready to check.

1

Solve x4+3=8\displaystyle \frac{x}{4}+3=8.

Check answerx = 20
2

Solve 5x − 7 = 2x + 11.

Check answerx = 6
3

Solve 3(2x + 1) − 4 = 11.

Check answerx = 2
4

Classify 4(x − 2) = 4x − 8.

Check answerInfinitely many solutions
04

Practice and tools

Use the resource that matches what you need next.

Worksheet

Solving Linear Equations

Thirty problems from one-step equations through applications.

Open resource Worksheet

Solving Multi-Step Equations

Practice distribution, like terms, and variables on both sides.

Open resource Quiz

Algebra 1 Readiness

Find strengths and gaps before moving forward.

Open resource