Chapter 8, Problem 30CR

To determine

The solution of the equation $\frac{2}{3}x+6=\frac{1}{3}x-13$ ,

Answer to Problem 30CR

  $x=-57$

Explanation of Solution

Given:

The equation, $\frac{2}{3}x+6=\frac{1}{3}x-13$

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 $\frac{2}{3}x+6=\frac{1}{3}x-13$ 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 $\frac{1}{3}x$ and then subtract both sides by $6$ and then multiply both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}\frac{2}{3}x+6=\frac{1}{3}x-13\\ \frac{2}{3}x+6-\frac{1}{3}x=\frac{1}{3}x-13-\frac{1}{3}x\\ \frac{1}{3}x+6=-13\\ \frac{1}{3}x+6-6=-13-6\\ \frac{1}{3}x=-19\\ \frac{1}{3}x\times 3=-19\times 3\\ x=-57\end{array}$

Thus, the solution of the given equation is $x=-57$ .