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How do you solve $-6n-10=-2n+4\left( 1-3n \right)$?

Last updated date: 14th Jun 2024
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Hint: To solve the given equation first we will open the parenthesis in the RHS and then shift all constant terms at the RHS and all the variable terms at the LHS. Then we will simplify the obtained equation by using the basic algebraic operations. Then we will get the value of $n$.

Complete step-by-step solution:
We have been given an equation $-6n-10=-2n+4\left( 1-3n \right)$
We have to solve the given equation.
Now, we know that the given equation is a linear equation in one variable and by solving the equation we get the value of $n$.
First we will open the parenthesis at the RHS we get
  & \Rightarrow -6n-10=-2n+4\left( 1-3n \right) \\
 & \Rightarrow -6n-10=-2n+4-4\times 3n \\
Now, performing the multiplication and simplifying further we get
$\Rightarrow -6n-10=-2n+4-12n$
Now, let us shift the constant terms at the RHS and variable terms at the LHS we get
$\Rightarrow -6n+2n+12n=4+10$
Now, solving the addition and subtraction we get
  & \Rightarrow -6n+14n=14 \\
 & \Rightarrow 8n=14 \\
Now divide the obtained equation by 8 to get the variable n at the LHS
\[\Rightarrow \dfrac{8n}{8}=\dfrac{14}{8}\]
Simplifying the obtained equation we get
\[\Rightarrow n=\dfrac{7}{4}\]
So on solving the equation $-6n-10=-2n+4\left( 1-3n \right)$ we get the value \[n=\dfrac{7}{4}\].

Note: To solve this type of questions we need to recall the linear equations and basic properties of linear equations. We can verify the answer by putting the value in the given equation. On solving the equation if we get the values of LHS and RHS equal it means that the answer is correct. We can also proceed with the given equation by taking out 2 common from both sides to get -3n-5=-n+(1-3n). Then we could have continued in a similar way as done above.