Solve the following equation -4 (2 - x) = 9.

Hint: In this question, we have been asked to find the value of x by using arithmetic operations on the given equality. Also, we need to solve the question by keeping in mind that there are possibilities of calculation mistakes, so we have to solve this question carefully.

Complete step-by-step solution -
In this question, we have to find the value of x by solving the equation, -4 (2 - x) = 9. In the given equation, we will first take the negative sign common from the term (2 - x). So, we will get,
(-4) [-(x - 2)] = 9.
We know that, when a negative term is multiplied by another negative term, the resultant will always be positive. So, we can write the equation as,
(4) (x - 2) = 9
Now, we will open the brackets. So, we will get,
4 x – 4 (2) = 9
4 x – 8 = 9
Now, we will keep the variable term on the left hand side and the constant values on the right hand side. So, we will get,
4 x = 9 + 8
4 x = 17
Now, we will divide both sides of the above equation by 4. So, we will get,
$\dfrac{\text{4x}}{\text{4}}\text{=}\dfrac{\text{17}}{\text{4}}$
$\Rightarrow \text{x=}\dfrac{\text{17}}{\text{4}}$
Hence, we get the value of x as $\dfrac{17}{4}$.

Note: The possible mistakes that the students can make in this question is by making calculation mistakes. That is, not keeping in mind the negative signs of numbers. The students can also solve this question by directly dividing the given equation by (-4) and then by further simplifying.