Question

If we add 7 to twice a number, we get 49. Find the number.

Answer 1

Hint:
Here, we have to find the number. We will assume the number to be some variable. We will frame a linear equation in one variable by using the given information. We will then solve the equation to get the required number.

Complete step by step solution:
We are given that if we add 7 to twice a number, we get 49.
Let \[x\] be the number.
We are given that twice a number, so the number has to be multiplied by 2.
So, twice the number becomes \[2x\].
Now, we are given that 7 is added to twice a number. So, we get the expression \[2x + 7\].
Now, we are given that if 7 is added to twice a number, we get 49.
So, equating the expression to 49, we get
\[2x + 7 = 49\]
Subtracting 7 from both sides, we get
\[ \Rightarrow 2x = 49 - 7\]
\[ \Rightarrow 2x = 42\]
Dividing by 2 on both the sides, we get
\[ \Rightarrow x = \dfrac{{42}}{2}\]
\[ \Rightarrow x = 21\]

Therefore, the number is \[21\].

Note:
We know that a linear equation is defined as an equation with the highest degree as one. Linear equations are a combination of constants and variables. Constants are the numbers whereas variables are represented in letters. We should also know that every linear equation in one variable has a one and unique solution. We can solve the linear equation easily. First, we have to put the variable on the left-hand side and the numerical values on the right-hand side and then Change the operators while changing sides of the terms we can solve for the variable.