91Ó°ÊÓ

Solving equations is a fundamental concept in algebra that involves finding the value(s) of unknown variables that make the equation true. In this exercise, we deal with the formula: \[ d = \frac{2S}{n(a + L)} \]Our goal is to find the value of \( S \) when other variables are given. Here is the step-by-step guide:

• Start by understanding the formula and identifying the variable to solve.
• Apply algebraic operations to simplify the equation.
• Make sure all similar terms are grouped together for clarity.

This method makes the equation easier to handle, leading us to a solution. Algebraic manipulation is key in this process.

Isolating the variable means separating the variable of interest on one side of the equation. Here's how it works in our given problem:We start with the formula:\[ d = \frac{2S}{n(a+L)} \]To isolate \( S \), we first eliminate the denominator by multiplying both sides by \( n(a + L) \): \[ d \cdot n(a + L) = 2S \]This operation helps to clear the fraction, making the equation simpler. Next, we further isolate \( S \) by dividing both sides by 2: \[ S = \frac{d \cdot n(a + L)}{2} \]This results in \( S \) being alone on one side of the equation. The key steps include identifying the operations needed and executing them systematically. This principle is widely used across various types of algebraic problems.

Formula rearrangement involves changing the structure of an equation to solve for a specific variable. This is done by using basic algebraic operations like multiplication, division, addition, and subtraction. Here’s how we tackle it in the given exercise:Starting with: \[ d = \frac{2S}{n(a + L)} \]Our first objective is to make \( S \) the subject of the equation. By multiplying both sides by \( n(a + L) \), we eliminate the fraction: \[ d \cdot n(a + L) = 2S \]Finally, we rearrange the formula by dividing both sides by 2: \[ S = \frac{d \cdot n(a + L)}{2} \]This rearrangement gives us a clear expression for \( S \). Rearranging formulas is a powerful tool in algebra, making complex equations manageable by systematically breaking them down into simpler parts.