A LITTLE LIGHTBULB MOMENT
Quantitative reasoning: algebra, functions and geometry
Solve a linear equation by isolating the variable
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Balance the seesaw, then read x’s weight.
The idea behind the cue
For a one-variable linear equation, use inverse operations on both sides to preserve equality. Simplify first if needed, then isolate the variable step by step. This works for ordinary linear equations, but equations with radicals or variables in denominators may need extra domain checks.
Practice this flashcard →Make it memorable
Short & simple
Balance the seesaw, then read x’s weight.
Acronym
SSI — Sparkly Sloths Idle.
Story
A clown stands on a seesaw loaded with the same weight on both sides. He removes two identical bags from each side, then splits the leftovers into equal boxes. The hidden box label is x, and once the seesaw stays level, x is easy to read.
Connect the pieces
- S (Sparkly) → Simplify: Simplify the equation first if needed by clearing clutter and combining obvious pieces.
- S (Sloths) → Subtract/Add: Use inverse operations on both sides to move constants away from the variable.
- I (Idle) → Isolate: Keep undoing operations until the variable stands alone.
- Sparkly · Simplify: Simplify the equation first if needed by clearing clutter and combining obvious pieces.
- Sloths · Subtract/Add: Use inverse operations on both sides to move constants away from the variable.
- Idle · Isolate: Keep undoing operations until the variable stands alone.
Know the limits
Applies to ordinary linear equations; equations with denominators or radicals may require additional restrictions.
Further reading · OpenStax science and mathematics textbooks ↗Check your understanding
Solve 3x + 5 = 20.
A. x = 15
B. x = 7
C. x = 25
D. x = 5
Reveal explanation
x = 5
Subtract 5 from both sides to get 3x = 15, then divide by 3. So x = 5.