1Cademy - Solving $$7(n - 3) - 8 = -15$$ Using a General Strategy

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Solving $7(n - 3) - 8 = -15$ Using a General Strategy

To solve the linear equation $7(n - 3) - 8 = -15$ using the general strategy, follow these steps:

Step 1. Simplify each side of the equation. Use the Distributive Property to remove the parentheses on the left side: $7n - 21 - 8 = -15$ . Combine the constant terms on the left: $7n - 29 = -15$ .

Step 2. Collect variable terms on one side. All variable terms ( $7n$ ) are already on the left side, so no action is needed here.

Step 3. Collect constant terms on the other side. Add $29$ to both sides to move the constant away from the variable: $7n - 29 + 29 = -15 + 29$ , yielding $7n = 14$ .

Step 4. Make the coefficient of the variable term equal to $1$ . Divide both sides by $7$ : $\frac{7n}{7} = \frac{14}{7}$ , giving $n = 2$ .

Step 5. Check the solution. Substitute $2$ for $n$ in the original equation: $7(2 - 3) - 8 = -15$ , which simplifies to $7(-1) - 8 = -15$ , and then $-7 - 8 = -15$ , resulting in $-15 = -15$ .

Since this is a true statement, the solution checks correctly.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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