Question

How do you solve $ - 5y - 5\left( { - 6 - 2y} \right) = 0 $ ?

Answer 1

Hint: This question is related to linear equation concept. An equation for a straight line is known as a linear equation. The term which is involved in a linear equation is either a constant or a single variable or product of a constant. The two variables can never be multiplied. This given question deals with a specific type of linear equation and that is, formulas for problem solving. Here in this question, we will first have to isolate the term $ y $ and then simplify it using distributive property to get the desired answer.

Complete step-by-step solution:
Given is $ - 5y - 5\left( { - 6 - 2y} \right) = 0 $
We have to solve the given equation in order to find the value of $ y $ for which left-hand side is equal to the right-hand side of the equation.
Let us simply start by simplifying the given equation using distributive property.
 $
   \Rightarrow - 5y - 5\left( { - 6 - 2y} \right) = 0 \\
   \Rightarrow - 5y - 5\left( { - 6} \right) - 5\left( { - 2y} \right) = 0 \\
   \Rightarrow - 5y + 30 + 10y = 0 \\
  $
Next, let us combine the like terms and then arrange them in such a way that variables and constants are opposite to the equal to sign and we get,
 $
   \Rightarrow 10y - 5y + 30 = 0 \\
   \Rightarrow 5y + 30 = 0 \\
   \Rightarrow 5y = - 30 \\
  $
Now, we divide both the sides of the equation by\[5\]and we get,
 $
   \Rightarrow \dfrac{{5y}}{5} = \dfrac{{ - 30}}{5} \\
   \Rightarrow y = - 6 \\
  $
Therefore, the value of $ y $ is $ - 6 $ .

Note: Now that we know the value of $ y $ is $ - 6 $ , there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of $ y $ in the given equation,
 $
   \Rightarrow - 5\left( { - 6} \right) - 5\left( { - 6 - 2\left( { - 6} \right)} \right) = 0 \\
   \Rightarrow 30 - 5\left( { - 6 + 12} \right) = 0 \\
   \Rightarrow 30 - 5\left( 6 \right) = 0 \\
   \Rightarrow 30 - 30 = 0 \\
   \Rightarrow 0 = 0 \\
  $
Now, the left-hand side is equal to the right-hand side of the equation. So, we can conclude that our solution or the value of $ y $ which we calculated was correct.