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Linear equations are statements that relate a variable with constant terms. In this case, the equation given is \(8h = 0\). Our main goal with linear equations is to determine the value of the variable that makes the equation true. By solving, we mean finding all values of the variable that transform the equation into a true statement.Linear equations often have one solution, but depending on the structure, they can also have no solution or infinitely many solutions. For example, if all terms were consistent and simplified to zero, indicating potentially infinite solutions. However, when a non-zero number equals zero, it indicates no solutions. In our given task, we were dealing with the simple linear equation \(8h = 0\), where there is a singular straightforward solution.

Isolating the variable is a critical step in solving linear equations. It involves manipulating the equation to express the variable explicitly on one side of the equation, usually in terms of constants or coefficients. In our example, the equation is \(8h = 0\).

• The variable, in this case \(h\), is multiplied by 8.
• To isolate \(h\), we divide both sides of the equation by 8.
• This gives us \(h = \frac{0}{8}\).

When simplifying \(\frac{0}{8}\), we observe that any number multiplied by zero results in zero. Therefore, \(h\) simplifies to 0. This step is crucial because isolating the variable allows us to clearly see the value that satisfies the equation.

Verifying the solution of an equation ensures that no mistakes were made during the calculation. This involves substituting the obtained value back into the original equation to see if it holds true. It's an essential check that confirms the accuracy of our solution.Let us verify the solution for our example where \(h = 0\):

• Substitute the value of \(h\) back into the original equation \(8h = 0\).
• This becomes \(8(0) = 0\).
• Simplifying the left side gives us 0, which equals the right side.

Since both sides of the equation are equal, our solution is verified as correct. Verification steps are particularly helpful in ensuring that division and simplification were executed correctly, especially in more complex equations.