Chapter 4.7, Problem 7WE

To determine

To solve the equation $A=2a^2+4ah$ , for h .

Answer to Problem 7WE

  $h=\frac{A-2a^2}{4a},a\ne 0$

Explanation of Solution

Given:

The equation, $A=2a^2+4ah$

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 $A=2a^2+4ah$ for h , isolate the variable term h on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate h on right side, first subtract $2a^2$ from both sides and then simplify further by dividing $4a$ from both sides as shown below,

  $\begin{array}{c}A=2a^2+4ah\\ A-2a^2=2a^2+4ah-2a^2\\ A-2a^2=4ah\\ \frac{A-2a^2}{4a}=\frac{4ah}{4a}\\ \frac{A-2a^2}{4a}=h\\ \Rightarrow h=\frac{A-2a^2}{4a}\end{array}$

Thus, on solving for the indicated variable it gives $h=\frac{A-2a^2}{4a}$ .

Since it is a rational expression after solving for the indicated variable, so the denominator should not be zero. That is, $a\ne 0$ .