Question

-5n + 2(3 + 3n) + 1 = -6n - 14

Explanation:

Step1: Expand the parentheses

First, we expand the term \(2(3 + 3n)\) using the distributive property \(a(b + c)=ab+ac\). So, \(2(3 + 3n)=2\times3+2\times3n = 6 + 6n\). The original equation \(-5n+2(3 + 3n)+1=-6n - 14\) becomes \(-5n+6 + 6n+1=-6n - 14\).

Step2: Combine like terms on the left side

Combine the \(n\)-terms and the constant terms on the left side. For the \(n\)-terms: \(-5n+6n=n\). For the constant terms: \(6 + 1 = 7\). So the equation simplifies to \(n+7=-6n - 14\).

Step3: Add \(6n\) to both sides

To get all the \(n\)-terms on one side, we add \(6n\) to both sides of the equation. \((n+7)+6n=(-6n - 14)+6n\). Simplifying both sides: \(n+6n+7=-6n+6n - 14\), which gives \(7n+7=-14\).

Step4: Subtract 7 from both sides

Subtract 7 from both sides to isolate the term with \(n\). \((7n+7)-7=-14 - 7\). Simplifying, we get \(7n=-21\).

Step5: Divide both sides by 7

Divide both sides of the equation by 7 to solve for \(n\). \(\frac{7n}{7}=\frac{-21}{7}\), so \(n=-3\).

Answer:

\(n = - 3\)