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Solving Linear Equations

The Hook

The hunt for X.

What is it?

Isolating the variable to find its value.

Time Travel (History)

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

Cheat Code

Undo operations in reverse PEMDAS order (SADMEP).

Practice This Now!

The Field Guide

In 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.

In The Real World: 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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Booby Trap!

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

Real World Challenge
"A gym membership is $50 plus $10 per month. You spent $170 total. How many months?"
The Logic: 10m + 50 = 170. Subtract 50 -> 10m = 120. Divide by 10 -> m = 12 months.

Training Drills

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