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To solve an equation, we often need to use a method called substitution. This involves replacing a variable in the equation with a given number. In the exercise, we start by substituting the given number, which is 1, into the variable r in the equation, 2r + 6 = 8. So, when we substitute 1 for r, we get: 2(1) + 6 = 8.
By making this substitution, we transform the equation and make it easier to solve, as we're now dealing with actual numbers instead of variables.
Substitution is a fundamental step because it allows us to check whether a specific value satisfies the equation. If you're ever stuck, remember that substitution simplifies the equation and helps you move forward in finding the solution.

After substitution, the next step is to simplify the equation, which means performing the arithmetic operations on the left-hand side. In our exercise, we start with the equation after substitution: 2(1) + 6. The first thing to do is the multiplication: 2(1) equals 2. So, the equation now looks like this: 2 + 6 = 8.
This step is crucial because it reduces the expression to a simpler form, making it easier to see whether both sides of the equation are equal. Simplifying any equation involves breaking it down step-by-step, ensuring each operation is correctly performed. This clarity helps in identifying errors and confirms that we are on the right path to the solution.

Once the equation is simplified, the final step is to check if the left-hand side equals the right-hand side. For our exercise, we already simplified the left-hand side to 2 + 6. When we add these numbers together, we get 8.
Now, we compare the left-hand side (8) with the right-hand side (8). Since both are equal, this tells us that our substitution was correct and the given number, 1, is indeed a solution to the equation 2r + 6 = 8.
Checking the solution is essential because it verifies the accuracy of our work. It is always a good practice to compare both sides of the equation to ensure they match. If they do, we've found a valid solution; if not, we need to recheck our steps.