College Algebra / Unit 3 Alg 133 worked example, 60 to 90 seconds
Solving a Linear Equation
The idea
Solving a linear equation means undoing what was done to the variable — clearing parentheses, collecting like terms, and applying inverse operations to both sides until the variable stands alone.
In practice
Solve 3x + 7 = 19. Subtract 7 from both sides — the additive inverse at work: 3x = 12. Divide both sides by 3 — the multiplicative inverse: x = 4. Substitute back: 3(4) + 7 = 19 — true, so 4 is the solution. Every legal move applies the same operation to both sides, which is why the balance never tips: the two sides stay equal at every line, and the last line reads the answer. Longer equations add moves, never new kinds of moves.
Where people slip
An operation applied to one side manufactures a different equation with a different answer.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
Something wrong in this lesson? Flag it · Sources for College Algebra