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In this tutorial, the focus is on rewriting formulas to solve for different variables. For example, in the equation distance = rate times time, we may solve for rate or time. To solve for a variable, isolate it by using basic algebraic rules like subtracting or dividing. For instance, to solve for x, subtracting 10 from both sides gives 5x = 65, then dividing by 5 results in x = 13. Similarly, in another example, subtracting B from both sides leads to the equation ax = C - B. These algebraic principles can be applied to various equations to solve for different variables efficiently.