Concept explainers
(a)
The equation
(a)
Answer to Problem 39HP
Explanation of Solution
Given information:
The equation:
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 formula for x, first multiply both sides by xy, then subtract x from both sides and then divide both sides by (ny-1) to simplify further as shown below:
Thus, the formula for the variable is
(b)
The equation
(b)
Answer to Problem 39HP
Explanation of Solution
Given information:
The equation:
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 for the variable y, first multiply both sides by (x-y), then again multiply both sides by 2, then subtract 2x from both sides , then add y both sides and then divide both sides by 3 to simplify further as shown below:
Thus, the formula for the variable is
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