"Solving for r" entails isolating the variable r on one side of the equation, typically in the form of "r = something" or "something = r". In the equation "5 3/4 = r/3", r is not isolated because it's divided by 3. To isolate r, we perform the opposite operation of division, which is multiplication. Maintaining balance, we apply the same operation to both sides of the equation.
Multiplying r/3 by 3 yields r(3/3) = r(1) = r. On the other side, we can calculate 3 * 5 = 15 and 3 * 3/4 = 9/4 = 2 1/4, thus 17 1/4. Alternatively, 5 3/4 can be expressed as 20/4 + 3/4 = 23/4, and multiplying by 3 gives 69/4 = 17 1/4.
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