Chapter 8.4, Problem 40IP

To determine

The solution of the equation $18=\frac{3}{4}(2w-1)$ .

Answer to Problem 40IP

  $w=12\frac{1}{2}$

Explanation of Solution

Given:

The equation, $18=\frac{3}{4}(2w-1)$ .

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 $18=\frac{3}{4}(2w-1)$ for the unknown variable, first multiplying 3/4 inside the bracket, now the equation is as shown below:

  $\begin{array}{l}18=\frac{3}{4}(2w-1)\\ 18=\frac{6w}{4}-\frac{3}{4}\end{array}$

Here to isolate w on right side, first add 3/4 both sides and then multiply both sides by 4/6 and then simplify further as shown below,

  $\begin{array}{l}18=\frac{6w}{4}-\frac{3}{4}\\ 18+\frac{3}{4}=\frac{6w}{4}-\frac{3}{4}+\frac{3}{4}\\ \frac{75}{4}=\frac{6w}{4}\\ \frac{75}{4}\times \frac{4}{6}=\frac{6w}{4}\times \frac{4}{6}\\ \frac{25}{2}=w\\ 12\frac{1}{2}=w\end{array}$

Thus, the solution of the given equation is $w=12\frac{1}{2}$ .