Chapter 1.3, Problem 46PPS

To determine

To find the value of x

  $x+\frac{3}{4}=3+\frac{3}{4}$ , and to name the property used.

Answer to Problem 46PPS

  $x=3$

And the main property used is subtraction property of equality.

Explanation of Solution

Given:

  $x+\frac{3}{4}=3+\frac{3}{4}$

Concept Used:

• Additive inverse property: $a-a=0$
• Subtraction property of equality:

$\begin{array}{c}x+a=b+c\\ \Rightarrow x+a-a=b+c-a\end{array}$

Calculation:

To find the value of x

  $x+\frac{3}{4}=3+\frac{3}{4}$ , and to name the property used.

Use subtraction property of equality.

  $\begin{array}{c}x+\frac{3}{4}=3+\frac{3}{4}\\ \Rightarrow x+\frac{3}{4}-\frac{3}{4}=3+\frac{3}{4}-\frac{3}{4}\\ \Rightarrow x+0=3+0;\text{ using additive inverse property}\text{.}\\ \Rightarrow x=3\end{array}$

Thus, for given equation $x=3$ . And the main property used is subtraction property of equality.