Chapter 1.1, Problem 45E

To determine

To Identify : Property of equality that makes the both equations are equivalent.

Answer to Problem 45E

Multiplication Property of Equality.

Explanation of Solution

Given information : Two equations:

  $\begin{array}{l}x-\frac{1}{2}=\frac{x}{4}+3---(1)\\ 4x-2=x+12---(2)\end{array}$

Here we use Multiplication Property of Equality.

In equation (1), multiply both the side by 4

  $4\cdot \left(x-\frac{1}{2}\right)=4\cdot \left(\frac{x}{4}+3\right)$

Now use distributive property

Distribute the 4 over the parenthesis

  $4x-4\cdot \frac{1}{2}=4\cdot \frac{x}{4}+4\cdot 3$

Simplify

  $4x-2=x+12$

Resultant equation this same as equation (2).