Question

How do you solve $\dfrac{a}{{ - 7}} - 7 = 5$?

Answer 1

Hint: Here we need to proceed by using just the simple and easy method where we just need to know that when we take the term from one side to the other side the sign changes. The sign becomes and multiplication changes to division. By using this rule we can easily find here the value of the required variable which is $a$.

Complete step by step solution:
Here we are given the equation where we need to find the variable $a$ from the given equation which is $\dfrac{a}{{ - 7}} - 7 = 5$.
So in order to solve this, we just need to know that when we take the term from one side to the other side the sign changes. The sign becomes and multiplication changes to division. By using this rule we can easily find here the value of the required variable which is $a$.
Now we have the equation as:
$\dfrac{a}{{ - 7}} - 7 = 5$
Taking $ - 7$ from Left hand side to right hand side, the sign of $ - 7$ will change from to
So we will get:
$
  \dfrac{a}{{ - 7}} = 5 + 7 \\
  \dfrac{a}{{ - 7}} = 12 \\
 $
Now we can write it as:
$\dfrac{a}{{ - 7}} = 12$
Now we need to find the value of $a$so we need to remove $ - 7$ which is in the denominator to the numerator $a$
As $ - 7$ is dividing the variable $a$ and if we take it from LHS to RHS this division will be converted to multiplication and we will get:
$
  \dfrac{a}{{ - 7}} = 12 \\
  a = ( - 7)(12) = - 84 \\
 $

Hence we get the value of the variable $a = - 84$

Note:
Here the student must know that as the sign changes when we move from LHS to RHS or from RHS to LHS, in a similar way the power also changes:
If we are given ${a^n} = b$ then we can write that $a = {b^{\dfrac{1}{n}}}$.