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Solving by Simplifying First
To solve the equation $5(n - 4) - 4n = -8$, follow a step-by-step strategy to simplify both sides before isolating the variable:
- Simplify the left side: First, use the distributive property to eliminate the parentheses by multiplying 5 by each term inside: $5n - 20 - 4n = -8. Next, use the Commutative Property to rearrange the terms so like terms are grouped together ($5n - 4n - 20 = -8), and combine those like terms to fully simplify the left side to . The right side is already simplified as . The equation is now .
- Isolate the variable: Undo the subtraction by applying the Addition Property of Equality. Add 20 to both sides () and simplify to find the value of : .
- Check the solution: Substitute 12 for back into the original equation to confirm it produces a true statement: $5(12 - 4) - 4(12) = -8, which simplifies to $5(8) - 48 = -8, and then $40 - 48 = -8-8 = -8n = 12$ is indeed the correct solution.
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Ch.2 Solving Linear Equations and Inequalities - Elementary Algebra @ OpenStax
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Learn After
A project manager is calculating the remaining budget (n) using the equation 5(n - 4) - 4n = -8. According to the standard strategy for solving linear equations, what is the first step required to simplify the left side of this equation?
A project coordinator is using the equation 5(n - 4) - 4n = -8 to determine the number of hours (n) allocated for a specific task. Arrange the following steps in the correct order to solve for n using the strategy of simplifying the equation first.
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Strategic Simplification of Linear Equations
A warehouse manager is using the equation $5(n - 4) - 4n = -8n) for a new shipment. To simplify the equation, the manager first applies the distributive property to the left side. Fill in the blank to complete the resulting intermediate equation: $5n - ____ - 4n = -8.
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A production supervisor uses the equation $5(n - 4) - 4n = -8nn$?
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