Question

If 4 more than twice a number is 6 less than that number. What is the number?

Answer 1

Hint: We will consider the number be x. This given question above will frame an equation with one variable for us. It has two conditions equated with each other. We will frame an equation using the conditions and solving it we will get to know the number.

Complete step-by-step answer:
Let the number be x.
Now the first condition is “ 4 more than twice a number”. Now twice the number is 2x and four more than that means \[2x + 4\]
Next is given that the above condition is “ 6 less than that number”. Thus we can write, \[x - 6\]
Now the equation will be,
\[2x + 4 = x - 6\]
Taking the variable on one side and transposing the constants on other side we get,
\[2x - x = - 6 - 4\]
On solving,
\[x = - 10\]
Thus that number so required is -10.
So, the correct answer is “-10”.

Note: Note that the equation we frame is totally the main part of the question. Some students fail only there in framing and then in spite of solving it we get the wrong answer. So like here some may frame the equation as, \[2\left( {4 + x} \right) = x - 6\] since they first make 4 more conditions and then twice of that whole condition. But given is twice of the number only. So be careful while reading and applying the conditions.
We can cross verify by putting the value of x in the framed equation.