How do you solve equations of the type `a=b/(cx)` ?
As usual in algebra, there are many different ways. Hee is one that always works -- though it may not be the most efficient for every problem.
`a=b/(cx)` Given equation
`a*x/1=b/(cx)*x/1` Multiply both sides by the same quantity. Note that the x's cancel on the right hand side.
`1/a*ax=1/a*b/c` Multiply both sides by 1/a, or divide by a.
`x=b/(ac)` This is the solution.
Check: `200/(4(10))=200/40=5` as required.
You will want to learn why the steps work; you do not want to try to memorize the final form of the answer.
Well AtTom'sRiver, x doesn't need to be alone. In the placeholder equation A=B/Cx, A, B, and C are holding the place of numbers. So, let's look at the placeholder equation and then we'll substitute it with the first equation: 5=200/4x.
A = B/Cx
A and B are constants, and C is a coefficient of x.
A(Cx) = B(Cx)/Cx
To get rid of the denominator (division), we multiply (the opposite of division) both sides of the equal sign by Cx.
A(Cx) = B
On the right side of the equal sign, Cx in the numerator cancels with the Cx in the denominator. On the left side of the equal sign, Cx is multiplied by A, because what you do on one side you must do to other side.
ACx = B
Carry out the multiplication of the constant A and the coefficient C. Now, we'll want to isolate the variable x.
ACx/AC = B/AC
To get rid of the coefficient AC, divide both sides of the equal sign by AC.
x = B/AC
This is what we are left with! Now here is the substitution:
A=5; B=200; C=4
x = 200/(5)(4)
x = 200/20
x = 10