Example

Solving 5(n−4)−4n=−8{}5(n - 4) - 4n = -8 by Simplifying First

To solve the equation 5(n−4)−4n=−85(n - 4) - 4n = -8, follow a step-by-step strategy to simplify both sides before isolating the variable:

  1. Simplify the left side: First, use the distributive property to eliminate the parentheses by multiplying 5 by each term inside: 5n−20−4n=−85n - 20 - 4n = -8. Next, use the Commutative Property to rearrange the terms so like terms are grouped together (5n−4n−20=−85n - 4n - 20 = -8), and combine those like terms to fully simplify the left side to n−20n - 20. The right side is already simplified as −8-8. The equation is now n−20=−8n - 20 = -8.
  2. Isolate the variable: Undo the subtraction by applying the Addition Property of Equality. Add 20 to both sides (n−20+20=−8+20n - 20 + 20 = -8 + 20) and simplify to find the value of nn: n=12n = 12.
  3. Check the solution: Substitute 12 for nn back into the original equation to confirm it produces a true statement: 5(12−4)−4(12)=−85(12 - 4) - 4(12) = -8, which simplifies to 5(8)−48=−85(8) - 48 = -8, and then 40−48=−840 - 48 = -8, resulting in the true mathematical statement −8=−8-8 = -8. Thus, n=12n = 12 is indeed the correct solution.

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Updated 2026-04-21

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