Think about how each operation is affecting the others in the equation. Would the instructions given undo the operations implicated in the equation?
No.
Practice makes perfect
Given the equation
d-3/5 = 6,we are asked if we can solve it by adding 3 before multiplying by 5. To verify if that would work, let's follow the suggested instructions to see what we get. We need to think about d-3 as a quantity in the numerator. If we solved this properly, complying with the Properties of Equality, but adding 3 first, we would have the work shown below.
As we can see, doing the inverse operations in that order does not isolate x in an efficient manner. This is because the 5 in the denominator is affecting the result of d-3. Therefore, we need to undo the division by 5 first. Thus, the first step must be multiplying by 5.
As we can see, this effectively isolates the variable d as needed.
Extra
Completely WRONG Way
If we were to completely forget to treat the numerator as a singular quantity, as though d and 3 were completely different entities, we would not obtain the same answer. We found above that the correct answer is d=33. Let's substitute this answer into the original equation and pretend as though the suggested method might work.
Remember, the above solution is done incorrectly. This does not follow the Properties of Equality and it does not follow the order of operations. We need to always follow the order of operations, respect the quantities created by numerators and denominators of fractions, and mind the Properties of Equality.
