Chapter 4.7, Problem 5OE

To determine

To solve the equation $a=\frac{x}{b^2}$ , for x .

Answer to Problem 5OE

  $x=a{b}^2$

Explanation of Solution

Given:

The equation, $a=\frac{x}{b^2}$

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.

Calculation:

To solve the given equation $a=\frac{x}{b^2}$ for x , 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 right side, multiply both sides by $b^2$ and then simplify further as shown below,

  $\begin{array}{c}a=\frac{x}{b^2}\\ a\cdot b^2=\frac{x}{b^2}\cdot b^2\\ a\cdot b^2=x\\ \Rightarrow x=a{b}^2\end{array}$

Thus, on solving for the indicated variable it gives $x=a{b}^2$ .