Chapter 1, Problem 14CR

To determine

To solve: the equation $3\left(n+4\right)=\frac{1}{2}\left(6n+4\right)$ .

Answer to Problem 14CR

No solution

Explanation of Solution

Concept used:

Distributive property:

  $a\left(b+c\right)=ab+bc$

Consider the given equation:

  $3\left(n+4\right)=\frac{1}{2}\left(6n+4\right)$

Apply the distributive property,

  $3n+12=3n+2$

Subtract $3n$ from both sides,

  $\begin{array}{c}3n+12-3n=3n+2-3n\\ 3n-3n+12=3n-3n+2\\ 12=2\end{array}$

But the statement $12=2$ is never true.

Hence, the given equation has no solution.