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After solving an equation, it's not just about finding a number that could potentially be a solution. It's crucial to check your answer to ensure accuracy. Here's how you can do that:- **Why Check?** Verifying your solution helps confirm that it satisfies the original equation. This step ensures you haven't made an error during your calculations. Even small mistakes in steps can lead to a wrong solution, so always check.- **How to Check:** Plug the calculated value of the variable back into the original equation. After substituting the variable, both sides of the equation should be balanced, confirming the correctness of the solution.For example, in the equation \( t - 18 = 24 \), after finding \( t = 42 \), substitute back to get \( 42 - 18 = 24 \). Since this is true (both sides equal 24), your solution is verified as correct.

In algebra, to solve an equation usually translates to 'isolating the variable.' This means arranging the equation so the variable is by itself on one side of the equation.- **Why Isolate?** This process is essential because it helps to clearly see the value of the unknown quantity you are trying to solve for. - **How to Isolate:** You need to perform operations that will undo any additions, subtractions, multiplications, or divisions affecting the variable. Do this step-by-step and maintain balance in the equation by carrying out the operation on both sides.In the equation \( t - 18 = 24 \), adding 18 to both sides helps to isolate \( t \). This results in the equation \( t = 42 \), clearly showing the value of \( t \). It's like unpacking a box to reveal what's inside—once isolated, you clearly identify your solution.

The substitution method isn't just a standalone solving technique; it's also a fantastic tool for checking solutions, especially in linear equations.- **What is Substitution?** At its core, substitution involves replacing a variable with a known value or expression. When you've solved for a variable, you substitute back into the equation to verify your result.- **Using Substitution to Verify:** This method is particularly useful when multiple operations affect the variable. By substituting the value back into each part of the equation, you confirm that both sides equal each other, solidifying your solution.In the equation \( t - 18 = 24 \), once we assume \( t = 42 \), substitute back: \( 42 - 18 \). If it equates to 24, the substitution confirms our steps were correct, and the solution is correct and accurate.