Simplify: $3 (n - 4) + 2 (4 n - 5) = 5 (n + 2) + 16$

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Solution

We have, $3 (n - 4) + 2 (4 n - 5) = 5 (n + 2) + 16$
By distributive property, we know $x . (y + z) = x . y + x . z$ . Hence, applying the same in the given equation we get;
$\begin{array}{rcl} 3 n - 12 + 8 n - 10 & = & 5 n + 10 + 16 \\ 11 n - 22 & = & 5 n + 26 \end{array}$
Moving the variable terms on one side of the equation, we get;
$11 n - 5 n = 22 + 26 6 n = 48 n = \frac{48}{6} n = 8$
Hence, the value of $n$ is $8$ .

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