Question

How do you solve $ \dfrac{{y - 1}}{y} = 10 $ ?

Answer 1

Hint: To solve the given equation, first we should try to eliminate the denominator to make the equation simple. The given equation is a type of linear equation that works on simple addition and subtraction methods.

Complete step by step solution:
Given equation: $ \dfrac{{y - 1}}{y} = 10 $
We want to isolate $ y $ , so we use this series of steps:
First multiply both sides by $ y $ to eliminate the denominator to make the equation simple:
$ \dfrac{{y - 1}}{y}.y = 10.y $
Now, cancel out the $ y $ in the left hand side:
 $ \Rightarrow y - 1 = 10y $
Now, subtract $ y $ from both the sides:
$
   \Rightarrow y - 1 - y = 10y - y \\
   \Rightarrow - 1 = 9y \;
 $
Finally, divide both sides by 9 to find the $ y $ :
$ \Rightarrow \dfrac{{ - 1}}{9} = \dfrac{{9y}}{9} $
Now, cancel out the 9 of both numerator and denominator of right hand side:
$ \therefore y = - \dfrac{1}{9} $
So, the correct answer is “ $ \Rightarrow y = - \dfrac{1}{9} $ ”.

Note: To solve a simple linear equation, start by moving the numbers with a variable attached to one side of the equation and the numbers without a variable attached to the other side. To move a number to a different side, you need to subtract it from both sides. Next, divide both sides of the equation by the number in front of the variable.