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Eliminating fractions from an equation is a crucial step to simplify the problem. You often start with an equation containing a fraction, which can complicate calculations. To make things easier, we can eliminate the fraction by multiplying every term by the denominator of the fraction. This clears the fractions completely.

For example, if you have an equation such as \[ -3 = \frac{11r + 68}{3} \]Multiply each side of the equation by the denominator of the fraction, in this case, 3. This ensures that the fraction is gone:\[ -3 \times 3 = 3 \times \frac{11r + 68}{3} \] The equation simplifies as:\[ -9 = 11r + 68 \]Now you're left with a much simpler linear equation without fractions, making it easier to solve.

Once the fraction has been eliminated, the next step is to isolate the variable. Isolating the variable means rearranging the equation so that the variable you are solving for is on one side of the equation, and everything else is on the other side.

With the equation \[ -9 = 11r + 68 \], you want to have the term with the variable, in this case, 'r', all by itself. You can achieve this by performing inverse operations. Here, subtract 68 from both sides:\[ -9 - 68 = 11r \]Simplifying gives:\[ -77 = 11r \]By isolating the variable on one side, you are a step closer to finding its value.

After isolating the variable and solving the equation, it's important to check if your solution is correct. Checking solutions confirms the solution's accuracy and helps detect any errors you might have made.

Take the solution you found for the equation, substitute it back in, and verify. For instance, with the equation \[ -3 = \frac{11r + 68}{3} \]and your solution \( r = -7 \), replace \( r \) with -7:\[ 11(-7) + 68 = -77 + 68 = -9 \]Then the equation is:\[ -3 = \frac{-9}{3} \]The right side simplifies to -3, confirming that both sides are equal:\[ -3 = -3 \]This step assures that the value you calculated for the variable is indeed a valid solution to the equation.