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Solving equations is a fundamental skill in algebra. It involves finding the value of the variable that makes the equation true. In the case of the equation \( 8t + 5 = 5 \), we are tasked with determining the value of \( t \) that satisfies the equation.

The first step is to simplify the equation so that it is easier to manage. This often involves simplifying each side by performing operations such as addition, subtraction, multiplication, and division. These operations help in keeping the balance of the equation.

Once the equation is simplified, we can proceed to find the solution by isolating the variable, which is discussed in the next section. It's essential to perform the same operation on both sides of the equation to maintain equality. This foundational concept helps ensure the equation remains balanced while working toward a solution.

After simplifying the equation, isolating the variable is the next important step. The goal here is to get the variable on one side of the equation by itself. In our exercise, the variable is \( t \).

We start with the equation \( 8t + 5 = 5 \). To isolate \( t \), we first subtract 5 from both sides. This step gives us \( 8t = 0 \). Performing the same operation on both sides maintains the balance of the equation.

With the variable term now alone, we proceed to divide both sides by 8, resulting in \( t = 0 \). By isolating \( t \), we have effectively solved the equation.

• Subtracting constants to move them to the other side
• Dividing by the coefficient of the variable to solve

These actions help bring us closer to the solution in a clear, logical manner. Once the variable is isolated, we can check our work to ensure accuracy.

After finding a solution, it is crucial to check its validity. Checking solutions involves substituting the value you found back into the original equation to see if it holds true.

In our scenario, we determined \( t = 0 \) as the solution. To verify this, we replace \( t \) with 0 in the original equation: \( 8(0) + 5 = 5 \). Simplifying the left side gives \( 0 + 5 = 5 \), which matches the right side.

The equality confirms our solution is correct. Checking solutions is an excellent way to avoid mistakes and gain confidence in your problem-solving skills. It ensures that all previous steps in solving the equation were executed correctly. By double-checking your work, you can trust in the accuracy of your result.