Question

How do you solve $ 3n - 5 = - 8(6 + 5n) $ ?

Answer 1

Hint: In this question we have to solve for the value of $ n $ from the given linear equation of one variable. To solve the linear equation of one variable, we will first move all variables term to one side of the equation and all constant terms of the equation to the other side of the equation by performing necessary operations.

Complete step-by-step answer:
Let us try to solve this question in which we have to find the value of $ n $ in the given equation $ 3n - 5 = - 8(6 + 5n) $ .This is a linear equation in one variable. We will use BODMAS to simplify this equation. In this equation L.H.S is already simplified. We have to just simplify R.H.S of the given linear equation.
To simplify we will first open the bracket multiply bracket terms with $ - 8 $ . So we will get,
 $ 3n - 5 = - 8(6 + 5n) $
 $ 3n - 5 = - 8\times 6 + - 8\times 5n $
Now our equation will be
  $ 3n - 5 = - 48 - 40n $
Now we will take all variables term to L.H.S and constant terms to R.H.S. After reorganization of terms, our equation becomes
 \[
  3n + 40n = - 48 + 5 \\
  43n = - 43 \\
  n = - 1 \;
 \]
We can also crosscheck our solution by putting the value of $ n $ in the equation. So let’s check if we get a write value of $ n $ or not by putting the value of n in the given equation.
Putting $ n = - 1 $ , we get
 $
  3( - 1) - 5 = - 8(6 + 5( - 1)) \\
   - 3 - 5 = - 8(6 - 5) \\
   - 8 = - 8(1) \\
   - 8 = - 8 \;
  $
Since the value of both L.H.S and R.H.S are equal.
 Hence value of $ n = - 1 $ for the equation $ 3n - 5 = - 8(6 + 5n) $ .
So, the correct answer is “n=-1”.

Note: The questions in which we are given a linear equation in one variable and we have to solve for the value of the variable very easily. While solving for a linear equation in one variable you just have to be clear about the sign of constant and variable terms where most students make mistakes.