Question

Solve the equation if possible. $$ \frac{1}{2}(12 n-4)=14-10 n $$

Short answer

The solution to the equation is \( n = \frac{3}{4} \).

Step-by-step solution

Simplify the equation

First, distribute the \(\frac{1}{2}\) inside the parenthesis to simplify it into a single term: \(\frac{1}{2} * 12n - \frac{1}{2} * 4\) which simplifies to \(6n - 2\). The equation now is \(6n - 2 = 14 - 10n\).

Rearrange terms in equation

Now, send -10n to the left side of the equation and -2 to the right side to bring similar terms together. Adding 10n on both sides we have \(6n + 10n = 14 - 2\). Combining like terms we get \(16n = 12\).

Solve for the variable

Lastly, solve for variable 'n'. When 16n = 12, n = \(\frac{12}{16}\). Simplifying the right hand side by reducing the fraction, n = \(\frac{3}{4}\).