Chapter 4, Problem 10CR

To determine

To solve the equation $6-2\left(n-3\right)=12$ .

Answer to Problem 10CR

  $a.\left\{0\right\}$

Explanation of Solution

Given information:

The equation $6-2\left(n-3\right)=12$

Concept used:

Exponent properties: If a , b are real numbers and m , n are whole numbers, then

• Product Property: $a^m\cdot a^n=a^{m+n}$
• Power Property: ${\left(a^m\right)}^n=a^{m\cdot n}$
• Product to a Power Property: ${\left(ab\right)}^m=a^m{b}^m$

Calculation:

In order to solve the given equation, first subtract 6 from both sides and then divide both sides by $-2$ . And then simplify further by adding 3 on both sides as shown below,

  $\begin{array}{c}6-2\left(n-3\right)=12\\ 6-2\left(n-3\right)-6=12-6\\ -2\left(n-3\right)=6\\ \frac{-2\left(n-3\right)}{-2}=\frac{6}{-2}\\ n-3=-3\\ n-3+3=-3+3\\ n=0\end{array}$

Thus, the solution of the given equation is $\left\{0\right\}$ .