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Chapter 2: Problem 167

Solve the given formula for the specified variable. Solve the formula \(V=L W H\) for \(L\)

Short Answer

Expert verified
The solution is \( L = \frac{V}{W H} \).

Step by step solution

01

Identify the given formula

The given formula is the volume of a rectangular prism: \[ V = L W H \]
02

Identify the target variable

The objective is to solve for the variable \( L \).
03

Isolate the target variable

To solve for \( L \), divide both sides of the equation by \( W H \):\[ \frac{V}{W H} = \frac{L W H}{W H} \]
04

Simplify the equation

Cancel out \( W \) and \( H \) on the right-hand side of the equation to isolate \( L \):\[ L = \frac{V}{W H} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables
To solve an equation, often you need to isolate a specific variable. This means you want to get that variable by itself on one side of the equation. In our exercise, we are solving for the variable \( L \) in the volume formula of a rectangular prism: \[ V = L W H \]

Here鈥檚 a quick guide to isolate a variable:
  • Identify the variable you need to isolate.
  • Use inverse operations to move other terms to the other side of the equation.
  • Simplify the resulting equation.
For our formula:
  • First, identify \( L \) as the target variable.
  • To move \( W H \) to the other side, divide both sides of the equation by \( W H \).
  • This leaves us with \[ L = \frac {V}{W H} \], successfully isolating \( L \)!
With the variable isolated, you can easily interpret or compute the value as needed.
Volume of Rectangular Prism
Understanding the concept of volume is crucial in solving the exercise. The volume of a rectangular prism can be found using the formula \[ V = L W H \]. This formula states that volume \( V \) is the product of the length \( L \), width \( W \), and height \( H \).
  • Length (L): The longest side of the rectangle.
  • Width (W): The shorter side adjacent to the length.
  • Height (H): The vertical dimension perpendicular to the base.
To visualize, imagine a box. Its length, width, and height together determine how much space it occupies.

This formula is very handy in various real-life applications, such as packaging, storage, and construction. Evidently, understanding how to manipulate and derive different parameters, like isolating \( L \), can provide deep insights and problem-solving techniques in algebra.
Algebraic Manipulation
Algebraic manipulation refers to the process of rearranging and simplifying algebraic expressions and equations. It鈥檚 a fundamental skill in algebra that allows solving equations, isolating variables, and understanding relationships between different quantities.

In our original exercise, we applied algebraic manipulation to solve for \( L \):
  • We started with \( V = L W H \).
  • By dividing both sides by \( W H \), we used inverse operations to cancel out terms and simplify the equation.
  • This resulted in \[ L = \frac {V}{W H} \].
This systematic approach of using algebra to move terms around ensures clarity and precision when solving equations.

Key points for effective algebraic manipulation:
  • Understand inverse operations: addition vs. subtraction, multiplication vs. division.
  • Always perform the same operation on both sides of the equation to maintain equality.
  • Simplify whenever possible to make the equation more understandable.
Practicing these techniques will make algebraic problems more manageable and improve overall mathematical problem-solving skills.

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Most popular questions from this chapter

Solve. For each inequality, also graph the solution and write the solution in interval notation. $$ |7 x+2|+8<4 $$

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Solve. $$ 3|x-4|+2=11 $$

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