Why do we multiply (1-x) by both sides first in the equation 34500 / (1-x) = 47920?

Question

Simple question to a problem I seemingly can't find the answer to. In the equation:

34500 / (1-x) = 47920?

Why is it that we multiply both sides by (1-x) first and not divide both sides by 34500? I am confused as to which step I am supposed to take first when solving for X. How do I find out which steps to take first? PEMDAS?

Answer 1

Given an equation that includes expressions that include the value x, "solving for x" means to isolate x on the left side of the equals sign and a single value or an expression on the right side of the equals sign.

The process involved uses "complementary operations." That is, to undo an addition, we subtract. To undo a subtraction, we add. To undo a multiplication, we divide. To undo a division, we multiply.

Here are examples:

x + 5 = 29

x = 24 [subtract 5 from both sides]

22/x = 2 [with x ≠ 0]

22 = 2x [multiply by x]

11 = x

x = 11 [still, x ≠ 0]

So,

34500 / (1-x) = 47920 [x ≠ 1]

34500 = 47920 * (1-x) [multiply both sides by (1-x)

34500 = 47920 - 47920x [distribute]

-13409 = -47920x [subtract 47920 from both sides]

13420 = 47920x [multipy both sides by (-1)]

47920x = 13420 [swith sides of equals]

x = 13420 / 47920 [divide both sides by 47920

x = 0.28005

The goal is to isolate x. [note: There is usually several ways to do this, but with the same answer.]

Answer 2

It's not so much a matter of PEMDAS as it is eliminating a divisor by distributive multiplication. By multiplying both sides by 1-x, that value can then be multiplied distributively to get 47920 - 47920x. Then, rather than dividing both sides by 34500, you subtract that value from both sides to get 0 = 13420 - 47920x, which leads to 47920x = 13420. At that point, you can then determine the fractional value of x.