Chapter 8, Problem 29CR

To determine

The solution of the equation $8.7w-3=5.5w+3.4$ ,

Answer to Problem 29CR

  $w=2$

Explanation of Solution

Given:

The equation, $8.7w-3=5.5w+3.4$

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 $8.7w-3=5.5w+3.4$ for the variable, isolate the variable term w on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate w on left side, first subtract both sides by $5.5w$ and then add both sides by $3$ and then divide both sides by $3.2$ and then simplify further as shown below,

  $\begin{array}{c}8.7w-3=5.5w+3.4\\ 8.7w-3-5.5w=5.5w+3.4-5.5w\\ 3.2w-3=3.4\\ 3.2w-3+3=3.4+3\\ 3.2w=6.4\\ \frac{3.2w}{3.2}=\frac{6.4}{3.2}\\ w=2\end{array}$

Thus, the solution of the given equation is $w=2$ .