Chapter 1.1, Problem 45E

To determine

To identify the property of equality that makes the given equations equivalent

Answer to Problem 45E

All the properties.

Explanation of Solution

Given:

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

Equation 2: $4x-2=x+12$

Concept used:

When two equations are equal, if you add, subtract, multiply or divide the equation, it gives the same value.

Simplify both the equations.

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

  $\begin{array}{l}\Rightarrow x-\frac{1}{2}=\frac{x}{4}+3\\ \Rightarrow \frac{2x-1}{2}=\frac{x+12}{4}\\ \Rightarrow 4(2x-1)=2(x+12)\\ \Rightarrow 8x-4=2x+24\\ \Rightarrow 4x-2=x+12\end{array}$

Consider Equation 2, $4x-2=x+12$

Thus, both the equations are the same.

Conclusion:

Therefore, since both the equations are the same, it satisfies all the properties of equality.