Chapter 8.2, Problem 53PFA

To determine

the solution of the proportion $\frac{5x+3}{5}=\frac{7-2x}{3}$ .

Answer to Problem 53PFA

  $x=1.04$

Explanation of Solution

Given:

The proportion, $\frac{5x+3}{5}=\frac{7-2x}{3}$ .

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 $\frac{5x+3}{5}=\frac{7-2x}{3}$ 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 3 and then multiply both sides by 5 and then simplify the like terms and then add both sides by 10x and then subtract both sides by 9 and then simplify further divide both sides by 25 as shown below,

  $\begin{array}{c}\frac{5x+3}{5}=\frac{7-2x}{3}\\ \frac{3\cdot \left(5x+3\right)}{5}=\frac{7-2x}{3}\cdot 3\\ \frac{15x+9}{5}=7-2x\\ \frac{15x+9}{5}\cdot 5=5\cdot \left(7-2x\right)\\ 15x+9=35-10x\\ 15x+9+10x=35-10x+10x\\ 25x+9=35\\ 25x+9-9=35-9\\ 25x=26\\ \frac{25x}{25}=\frac{26}{25}\\ x=1.04\end{array}$

Thus, the solution of the proportion is $x=1.04$ .