Question

What number should both sides of the following equation be multiplied by in order to solve for x? x/6.5 = 4

Answer 1

I think you would multiply by the denominator 6.5 to isolate the variable.

Answer 2

When you are trying to solve for a variable in an equation you have to do the same operation on both sides. The basic idea/rule is that if you are trying to solve for a variable that is being multiplied by a number you will divide by such number since you are doing the "reverse" operation. With that said, we say that if the variable is being divided by a number both sides have to be multiplied by such number. In this case, the variable x is being divided by 6.5, so you have to multiply both sides by 6.5 to get the following
$\frac{x}{6.5} = 4 \\ 6.5\times \frac{x}{6.5} = 4 \times 6.5 \\ x = 26$