91Ó°ÊÓ

Solving equations is a fundamental skill in algebra that involves finding the value of the variable that makes the equation true. When you solve an equation, you're essentially trying to determine what number can replace the variable to balance both sides of the equation.

In the example provided:

\( x + 5 = 8 \)

We need to find the value of \( x \) to make the equation true. The key principle used here is the addition principle, which allows us to add or subtract the same value on both sides of an equation to simplify it.

1. Always start by identifying the equation and the terms involved.
2. Use the addition or subtraction principle to simplify each side step-by-step.
3. After isolating the variable, you will have the solution!

Isolating the variable means manipulating the equation such that the variable in question is alone on one side of the equation. This allows us to easily see its value.

In our example: \( x + 5 = 8 \), the goal is to get \( x \) by itself. Here's a simple breakdown of the process:

1. Identify the term that needs to be removed to isolate the variable.
2. Since \( +5 \) is added to \( x \), we subtract 5 from both sides to maintain the balance:

\[ x + 5 - 5 = 8 - 5 \]

3. Simplify both sides to get \( x \) alone:

\[ x = 3 \].

By isolating the variable, we find that \( x = 3 \). This process can be applied to more complex equations as well, involving multiple steps and additional operations.

Once you have found the solution to an equation, it's crucial to check that your solution is correct. This step ensures that the value obtained for the variable satisfies the original equation.

In our example, we found that \( x = 3 \). To check this solution:

1. Substitute \( x = 3 \) back into the original equation: \( 3 + 5 = 8 \).
2. Simplify the equation to see if both sides are equal:

\[ 3 + 5 = 8 \]
which simplifies to \[ 8 = 8 \].

3. Since both sides are equal, our solution \( x = 3 \) is indeed correct.

Checking your solution confirms accuracy and helps reinforce your understanding of solving equations. Always remember to perform this step for confidence in your answers!