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Solving Linear Equations

Overview

The hunt for X.

What is it?

Isolating the variable to find its value.

History

Ancient Egyptians solved these using the 'Method of False Position'.

Key Idea

Undo operations in reverse PEMDAS order (SADMEP).

Practice This Topic

Concept Guide

Plain English: The goal is to get X alone. It's like unwrapping a gift. If X is multiplied by 2 and then has 5 added to it, you must subtract 5 and then divide by 2.

Real-world example: Budgeting. 'I have $100. Tickets are $20. How many can I buy?' 20x = 100.

How to do it

  1. Simplify both sides (distribute/combine terms).
  2. Move variables to one side.
  3. Undo Addition/Subtraction.
  4. Undo Multiplication/Division.
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Common Pitfall

Forgetting to do the operation to BOTH sides of the equals sign. Balance the scale!

Word Problem
"A gym membership is $50 plus $10 per month. You spent $170 total. How many months?"
Reasoning: 10m + 50 = 170. Subtract 50 -> 10m = 120. Divide by 10 -> m = 12 months.

Practice Examples

Two Step
2x + 5 = 15 2x = 10 (-5) x = 5 (/2)
Subtract first, then divide.