Chapter 8, Problem 1VR

Complete each statement with the correct word or words from the column on the right. Some of the choices may not be used.

addition principle

multiplication principle

solution

equivalent

equation

inequality

Any replacement for the variable that makes an equation true is called a(n) ________of the equation.  [8.1a]

To determine

To Fill: The statement “Any replacement for the variable that makes an equation true is called a(n) _______ of the equation” with appropriate word by using given choices.

Answer to Problem 1VR

Solution:

Any replacement for the variable that makes an equation true is called a solution of the equation.

Explanation of Solution

Given Information:

The choices are addition principle, multiplication principle, solution, equivalent, equation and inequality.

Explanation:

The solution of the equation is the value of the variable which makes an equation true.

That is, the solution of the equation is any substitution for the variable that makes an equation true.

For example, consider an equation,

$x+3=8$

In the equation if the variable x is replaced by 5,

$\begin{array}{r}5+3\stackrel{?}{=}8\\ 8=8\end{array}$

As, the value 5 is the replacement of variable x which makes equation true.

So, 5 is the solution of the equation.

Therefore, any replacement for the variable that makes an equation true is called a solution of the equation.