91Ó°ÊÓ

When solving equations, isolating the variable you're looking for is essential. In our exercise, we need to solve for the variable T in the equation \[ V = \frac{L W T}{144} \].
To do this, we must get T by itself on one side of the equation. Start by identifying where T is located and then focus on eliminating the other terms around it. A practical approach to isolate T involves:

• Looking at what's attached to T (multiplication, division, etc.)
• Performing the opposite operation on both sides of the equation

In our example, T is multiplied by LW and divided by 144. To isolate T, we first multiply both sides by 144. This removes the fraction, leaving us with:
\[ 144V = L W T \]
Now we only need to get rid of LW by dividing both sides by LW. This results in:
\[ T = \frac{144V}{L W} \]
Isolating variables simplifies the problem and makes it easier to find the value of the unknown.

Algebraic manipulation involves rearranging equations to isolate variables. It includes basic operations like addition, subtraction, multiplication, and division. These steps often need to be done in a logical sequence.
In our given equation \[ V = \frac{L W T}{144} \], we needed to isolate T. Here's the detailed manipulation:

• We started with the division by 144. To cancel this, we multiplied both sides by 144:
• \[ 144V = L W T \]
• Next, T is still multiplied by LW. We need to cancel this by dividing both sides by LW:
• \[ T = \frac{144V}{L W} \]

This process required us to understand how to properly apply operations to ensure that both sides of the equation maintain equality.
Effective algebraic manipulation is pivotal when solving more complex equations, as it helps break them down into solvable parts.

Solving equations systematically enhances clarity and ensures accuracy. Here's an overview of the step-by-step process:
1. **Identify the Equation:** Understand the given equation. In our case, \[ V = \frac{L W T}{144} \].
2. **Isolate the Variable:** Determine which variable you need to solve for, then use operations to isolate it. Multiply or divide both sides as needed. In this exercise, multiplying both sides by 144 gave us:
\[ 144V = L W T \] 3. **Simplify the Equation:** Perform the necessary algebraic manipulations. Here, we divided both sides by LW, resulting in:
\[ T = \frac{144V}{L W} \] Following these steps ensures that you systematically approach the problem and check all necessary operations. Breaking down each step helps avoid mistakes and makes complex problems manageable.