Question

How do you solve \[ - 6\left( {1 - 5v} \right) = 54\]?

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 \[v\] and then simplify it to get the desired answer.

Complete step-by-step solution:
Given is \[ - 6\left( {1 - 5v} \right) = 54\]
We have to solve the given equation in order to find the value of \[v\] for which left-hand side is equal to the right-hand side of the equation.
Let us simply start by simplifying the given equation by dividing \[ - 6\] from both sides of the equation.
\[
   \Rightarrow \dfrac{{ - 6\left( {1 - 5v} \right)}}{{ - 6}} = \dfrac{{54}}{{ - 6}} \\
   \Rightarrow 1 - 5v = - 9 \\
 \]
Next, let us arrange the terms in such a way that variables and constants are opposite to the equal to sign and we get,
\[
   \Rightarrow 1 + 9 = 5v \\
   \Rightarrow 10 = 5v \\
 \]
Now, we divide both the sides of the equation by \[5\] and we get,
\[
   \Rightarrow \dfrac{{10}}{5} = \dfrac{{5v}}{5} \\
   \Rightarrow 2 = v \\
 \]
Therefore, the value of \[v\] is \[2\].

Note: Now that we know the value of \[v\] is \[2\], there is a way to double check our answer. In order to double check the solution we are supposed to substitute the value of \[v\] in the given equation,
\[
   \Rightarrow - 6\left( {1 - 5v} \right) = 54 \\
   \Rightarrow - 6\left( {1 - 5\left( 2 \right)} \right) = 54 \\
   \Rightarrow - 6\left( {1 - 10} \right) = 54 \\
   \Rightarrow - 6\left( { - 9} \right) = 54 \\
   \Rightarrow 54 = 54 \\
 \]
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 v which we calculated was correct.