Question

Solve the algebraic equation: $5n + 34 = \,\, - 2(1 - 7n)$

Answer 1

Hint: The given equation is a linear equation that has the same one variable on both sides of the separating ‘equals to’ sign. So we apply the BODMAS rule and combine the like terms together and separate the constants on the other side. This way we would get the value of the variable.

Complete step by step answer:
Firstly, we write down the equation provided in the question
$5n + 34 = \,\, - 2(1 - 7n)$
As we can see the highest power of the variable present in the question is one. This means the equation is linear in nature with variables on both sides of it.
Now we apply the BODMAS rule on the left side of the equation
BODMAS Rule: BODMAS is an acronym that stands for “Bracket-Order (Powers & Square Roots)-Division-Multiplication-Addition-Subtraction”. It provides us the order to operate on mathematical expressions and the method to open all three kinds of brackets i.e. \[(\,\,\,)\,\,,\,\,\{ \,\,\,\} \,,\,\,[\,\,\,]\,\,\,\] in a way that bigger bracket first then middle one and finally the small bracket.
 Given that the expression is a linear equation and has only one bracket, we solve the bracket first then move our like variables to one side of the equation like this
$
  5n + 34 = \,\, - 2(1 - 7n) \\
   \Rightarrow 5n + 34 = \,\, - 2 + 14n \\
   \Rightarrow 5n - 14n = \,\, - 2 - 34 \\
 $
Now it is easier for us to solve this with like terms together on each side of the equation
$
   \Rightarrow n(5 - 14) = - 36 \\
   \Rightarrow \; - 9n = \,\, - 36 \\
   \Rightarrow \,n = \dfrac{{ - 36}}{{ - 9}} = 4 \\
 $
So our solution for the equation is
$n = 4\,$

Note:
 Knowing the correct order of the operations helps us to evaluate the correct answer otherwise a glitch can occur. While solving an algebraic equation, containing variables and numbers, our goal is to find the value of a variable.