Question

If two times a number is equal to that number minus $4$, then find the number?
${\text{A}}. - 7$
\[{\text{B}}. - 6\]
${\text{C}}. - 4$
${\text{D}}. - 3$

Answer 1

Hint: From the given question, we have to find the unknown number. First, we assume the unknown number and make the mathematical expressions for the given if condition by using some variables then we get the actual unknown number and finally post the correct option from the given.

Formula used: Let us take the unknown number be ${\text{x}}$.
Let ${\text{n}}$ times of a number be expressed in the mathematical form be ${\text{nx}}$.
Let two times of that number be expressed as$2{\text{x}}$.
Let the number minus $4$ be expressed as ${\text{x}} - 4$.

Complete step-by-step answer:
According to the question, we had two times the number equal to that number minus $4$.
Now, we are going to frame the above by the given if condition as a mathematical equation. We get,
$2{\text{x}} = {\text{x}} - 4$
Now, keeping the variables on one side and numerical terms on the other side. So, we have to move ${\text{x}}$ to the left hand side (LHS). We get,
$ \Rightarrow 2{\text{x}} - {\text{x}} = - 4$
 While subtracting them, we will get,
$ \Rightarrow {\text{x}} = - 4$
  Therefore, the unknown number ${\text{x}}$ be $ - 4$ .

$\therefore $ The option C is the correct answer.

Note: The given question is very simple to solve only when the mathematical expressions are correct. The students concentrate on writing the mathematical expressions from the given information by clearly understanding the question.
There is another little hard way to find the answer but easy from the given options.
Our given mathematical expression is $ \Rightarrow 2{\text{x}} - {\text{x}} = - 4$ .
Now, we have to substitute the given option values $ - 7, - 6, - 4, - 3$one by one on the above expression.
 On substituting the values we going to get $ - 4$ on the left hand side (LHS) also because we already had $ - 4$ on the right hand side (RHS) we going to equalise the LHS and RHS.
If ${\text{x}} = - 7$, then we get $ \Rightarrow 2\left( { - 7} \right) - \left( { - 7} \right) = - 14 + 7 = - 7 \ne - 4$.
If ${\text{x}} = - 6$, then we get $ \Rightarrow 2\left( { - 6} \right) - \left( { - 6} \right) = - 12 + 6 = - 6 \ne - 4$.
If ${\text{x}} = - 4$, then we get $ \Rightarrow 2\left( { - 4} \right) - \left( { - 4} \right) = - 8 + 4 = - 4 = - 4$.
If ${\text{x}} = - 3$, then we get $ \Rightarrow 2\left( { - 3} \right) - \left( { - 3} \right) = - 6 + 3 = - 3 \ne - 4$.
Therefore, the option ${\text{C}}$ is the correct one because LHS and RHS are equal when applying the $ - 4$ numerical term on the mathematical expression.