Question

What is twice the sum of a number and 9 is equal to 7?

Answer 1

Hint: To obtain the solution we will form an equation using the information given in the question. Firstly as we don’t know the number we will let it as $x$ then according to the question we will add 9 to it and multiply it by 2. Finally we will put them equal to 7 and simplify it to get the value of \[x\].

Complete step-by-step answer:
The statement is given as what is twice the sum of a number and 9 is equal to 7.
So we will divide the statement in two parts
First part state that “Twice the sum of a number and 9”
Let the number is $x$ using above statement we get,
$2\left( x+9 \right)$….$\left( 1 \right)$
Next part state that “is equal to 7”
So we will put equation (1) equal to 7 and simplify it as below:
$\begin{align}
  & 2\left( x+9 \right)=7 \\
 & \Rightarrow 2x+18=7 \\
 & \Rightarrow 2x=7-18 \\
 & \therefore x=\dfrac{-11}{2} \\
\end{align}$
  Hence the number is $x=\dfrac{-11}{2}$

Note: An equation is an equal statement of two algebraic expressions with one unknown variable. In this case it is a Linear equation as the power of the unknown variable is 1. There are other terms in the equation other than unknown variables. The solution of the equation obtained is the value that satisfies the equation when we equate it in it. We can check whether our solution is correct or not by putting it in the equation and checking whether we get the value as 7.
Put $x=\dfrac{-11}{2}$ in equation (1) as:
$\begin{align}
  & 2\left( \dfrac{-11}{2}+9 \right) \\
 & \Rightarrow 2\left( \dfrac{-11+18}{2} \right) \\
 & \Rightarrow 2\times \dfrac{7}{2} \\
 & \Rightarrow 7 \\
\end{align}$
So we get the value 7 hence the solution is correct.