   # True or False? (a) Adding the same number to each side of an equation always gives an equivalent equation. (b) Multiplying each side of an equation by the same number always gives an equivalent equation. (c) Squaring each side of an equation always gives an equivalent equation. ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
Publisher: Cengage Learning
ISBN: 9781305071742
Chapter P.8, Problem 5E
Textbook Problem
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## True or False? (a) Adding the same number to each side of an equation always gives an equivalent equation. (b) Multiplying each side of an equation by the same number always gives an equivalent equation. (c) Squaring each side of an equation always gives an equivalent equation.

To determine

a)

To state:

True or false for the statement ‘adding the same number to each side of an equation always gives an equivalent equation’.

### Explanation of Solution

Approach:

Simplest type of equation is called a linear equation or first degree equation (power of x=1). An equation contains terms which is either a constant or a non-zero multiple of the variable.

We solve the equations by changing it to an equivalent equation with all variables on one side and all constants on the other side.

Ex: 5x+2=12

Here x is called the variable. A variable is usually represented as letters. Here x is unknown and need to find the value that makes the equation true. The values that make the equation true are called solutions or roots of the equation and the process of finding the values is called solving the equation.

Two equations with exactly same solution are called equivalent equations.

Properties of equality

To determine

b)

To state:

True or false for the statement ‘multiplying each side of an equation by the same number always gives an equivalent equation’.

To determine

c)

To state:

True or false for the statement ‘squaring each side of an equation always gives an equivalent equation’.

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