91Ó°ÊÓ

When solving linear equations, isolating the variable is a crucial first step. In our problem \(-8 = t - 2\), the goal is to have \(t\) on one side by itself. This means we need to perform operations that simplify the expression and leave \(t\) isolated. To start, you should look at the equation: currently, \(t\) is not isolated because it's being subtracted by 2.
To eliminate the -2, add 2 to both sides of the equation. Why both sides? Because whatever you do to one side, you must also do to the other to maintain equality. Here’s how it looks:

• Left side: \(-8 + 2\)
• Right side: \(t - 2 + 2\). This then simplifies to just \(t\)

So, the equation becomes \(-6 = t\).
This step of isolating the variable makes solving much simpler. With \(t\) by itself, you can easily see that \(t\) equals -6.

Verifying your solution ensures you've solved the equation correctly. Without verification, there's a risk of potential errors lurking in your calculations. Once you have isolated \(t\) and found its value, which is -6 in this case, the next step is to check if this solution satisfies the original equation.
To verify, substitute \(t = -6\) back into the original equation: \(-8 = t - 2\). When you replace \(t\) with -6, it becomes \(-8 = -6 - 2\). Simplifying the right side, you get:

• Right side: \(-6 - 2 = -8\)

Now compare both sides of the equation:

• -8 equals -8

Since they are equal, your solution is verified.
This process ensures that your calculations are correct and that your answer holds true for the given equation.

Equation simplification is the process of turning a complex equation into a simpler one. Why is this important? Simplifying an equation makes the math cleaner and clearer, allowing for easier manipulation and understanding of the relationships within.
In our example, the simplification occurs when we combined terms on each side:

• Original equation: \(-8 = t - 2\)
• After isolating \(t\), we simplify to: \(-6 = t\)

This simplification stemmed from performing operations that maintain equality — in this case, adding 2 to both sides. Remember, every simplification step should work toward isolating the variable.
Ultimately, simplification reduces the equation to its essence, highlighting the solution succinctly. This encompasses several important mathematical practices like combining like terms and performing inverse operations.
The goal is to make your final expression plain and clear — in this case, \(t = -6\), telling us exactly what value satisfies the original equation.