Chapter 6.4, Problem 25PPS

To determine

the solution of the proportion $\frac{6}{14}=\frac{7}{x-3}$ .

Answer to Problem 25PPS

  $x=19.33$

Explanation of Solution

Given:

The proportion, $\frac{6}{14}=\frac{7}{x-3}$ .

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 $\frac{6}{14}=\frac{7}{x-3}$ 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 both side, first multiply both sides by 14 and then multiply both sides by 6 and then add both sides by 18 and then simplify further we divide both sides by 6 as shown below,

  $\begin{array}{c}\frac{6}{14}=\frac{7}{x-3}\\ \frac{6}{14}\cdot 14=\frac{7}{x-3}\cdot 14\\ 6=\frac{98}{x-3}\\ 6\cdot \left(x-3\right)=98\\ 6x-18=98\\ 6x-18+18=98+18\\ 6x=116\\ \frac{6x}{6}=\frac{116}{6}\\ x=19.33\end{array}$

Thus, the solution of the proportion is $x=19.33$ .