Question

When $4$ times the number $x$ is added to $12$, the result is $8$. What number results when $2$ times $x$ is added to $7$ ?
A) $ - 1$
B) $5$
C) $8$
D) $9$

Answer 1

Hint: We will follow the given condition according to the question and solve the equations that will be generated by the condition. There will be two equations according to the question. From the first equation we will get the value of $x$ then substitute its value in the second equation and find the answer for the second condition given in the question.

Complete step-by-step solution:
The first condition is as follows:
$4$ times the number $x$ is added to $12$, the result is $8$
Converting it to equation form, we get:
$4x + 12 = 8$
Solving the above equation for the value of $x$ ,
$\Rightarrow 4x = 8 - 12$
$\Rightarrow 4x = - 4$
$\Rightarrow x = - 1$
Therefore, the value of $x$ is $ - 1$ .
The second condition is as follows:
What number results when $2$ times $x$ is added to $7$ ?
Converting it to equation form, we get:
$2x + 7 = ?$
We know the value of $x$ that we got from solving first condition, so know we substitute the value of $x$ we got in the second condition equation,
Substituting the value of $x = - 1$ in the equation,
$2( - 1) + 7$
$ = - 2 + 7$
$ = 5$
The value of the equation $2x + 7$ is $5$ .
So, the correct answer is option $B.$ $5$.

Note: This question is an example of a substitution equation. Here we substitute the value we found in one condition to another condition, so that it satisfies both the equations. Here the value of $x$ we got in the first condition is substituted in the second condition so as to satisfy both the equations given in the question.