Chapter 8.5, Problem 1GP

To determine

The solution of the equation $x+6=3x$ ,

Answer to Problem 1GP

  $x=3$

Explanation of Solution

Given:

The equation, $x+6=3x$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $x+6=3x$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, first subtract both sides by $x$ and then divide both sides by $2$ simplify further as shown below,

  $\begin{array}{c}x+6=3x\\ x+6-x=3x-x\\ 6=2x\\ \frac{6}{2}=\frac{2x}{2}\\ 3=x\\ \Rightarrow x=3\end{array}$

Thus, the solution of the given equation is $x=3$ .