Question

How do you solve \[\dfrac{1}{4}\left( {x - 3} \right) = - 2?\]

Answer 1

Hint: This question describes the operation of addition/ subtraction/ multiplication/ division. In this question, we would find the value of \[x\] . For making the easy calculation, we would arrange the \[x\] terms into one side and constant terms into another side. We need to know the arithmetic operation with the involvement of fraction terms. We need to know how to take LCM for fraction terms.

Complete step-by-step answer:
The given question is shown below,
 \[\dfrac{1}{4}\left( {x - 3} \right) = - 2 \to \left( 1 \right)\]
For making easy calculation we would solve the left-hand side of the equation at first,
In LHS we have,
 \[\dfrac{1}{4}\left( {x - 3} \right)\]
The above equation can also be written as,
 \[\dfrac{x}{4} - \dfrac{3}{4} \to \left( 2 \right)\]
Let’s substitute the above-mentioned equation in the equation \[\left( 1 \right)\] , we get
 \[\left( 1 \right) \to \dfrac{1}{4}\left( {x - 3} \right) = - 2\]
 \[\dfrac{x}{4} - \dfrac{3}{4} = - 2\]
Let’s move the term \[\dfrac{{ - 3}}{4}\] from the left side to the right side of the equation, so we get
 \[\dfrac{x}{4} = - 2 + \dfrac{3}{4}\]
 \[x = \left( { - 2 + \dfrac{3}{4}} \right) \times 4 \to \left( 3 \right)\]
For solving the above equation we would take LCM for \[\left( { - 2 + \dfrac{3}{4}} \right)\]
We have,
 \[\left( { - 2 + \dfrac{3}{4}} \right)\]
For the above term, we take LCM as \[4\]
So, we get
 \[\dfrac{{ - 2 \times 4}}{4} + \dfrac{3}{4}\]
The above equation can also be written as,
 \[\dfrac{{ - 8 + 3}}{4} = \dfrac{{ - 5}}{4}\]
So, we get
 \[\left( { - 2 + \dfrac{3}{4}} \right) = \dfrac{{ - 5}}{4} \to \left( 4 \right)\]
Let’s substitute the equation \[\left( 4 \right)\] in the equation \[\left( 3 \right)\] , we get
 \[\left( 3 \right) \to x = \left( { - 2 + \dfrac{3}{4}} \right) \times 4\]
 \[
  x = \dfrac{{ - 5}}{4} \times 4 \\
  x = - 5 \\
 \]
So, the final answer is,
 \[x = - 5\]
So, the correct answer is “ \[x = - 5\] ”.

Note: This question describes the operation of addition/ subtraction/ multiplication/ division. Note that to convert a mixed fraction term to a simple fraction term we can take LCM for that. To solve this type of question we would remember the following things,
When a negative number is multiplied with a negative number, the answer becomes positive.
 When a positive number is multiplied with a negative number, the answer becomes negative.
When a positive number is multiplied with the positive number the answer becomes positive.