Question

How do you write the expression for: the sum of twice a number and half the number is 10?

Answer 1

Hint: In this question, we assume the number first. Then read the question by dividing it into smaller parts. Here, it is given that twice a number, and half the number. Then the sum of twice a number and half the number is 10. This way we can construct the equation.

Complete step-by-step answer:
Let us assume that the number is x.
In the question, it is given that the sum of twice a number and half the number is 10.
Twice a number means to multiply the number with 2.
Therefore, it will become 2x.
Now, half the number means to divide the number by 2.
Therefore, it will become$\dfrac{x}{2}$.
The sum of these two numbers is 10.
$ \Rightarrow 2x + \dfrac{x}{2} = 10$
Here, we got the equation. Let us simplify this equation to find the value of x.
Now, let us find the least common multiple on the left-hand side.
$ \Rightarrow \dfrac{{4x + x}}{2} = 10$
Here, add the numerator on the left-hand side.
$ \Rightarrow \dfrac{{5x}}{2} = 10$
Let us multiply the above equation by 2 on both sides.
$ \Rightarrow \dfrac{{5x}}{2} \times 2 = 10 \times 2$
  So, we will get
$ \Rightarrow 5x = 20$
Now, let us divide the above equation by 5 into both sides.
$ \Rightarrow \dfrac{{5x}}{5} = \dfrac{{20}}{5}$
So,
$ \Rightarrow x = 4$

Note:
To check whether our answer is correct or not, substitute the value of x in the equation.
The equation is,
$ \Rightarrow 2x + \dfrac{x}{2} = 10$
Let us put the value of x is equal to 4 on the left-hand side of the equation.
$ \Rightarrow 2\left( 4 \right) + \dfrac{4}{2} = 10$
Now, simplify the above equation by applying multiplication and division.
 $ \Rightarrow 8 + 2 = 10$
That is equal to
$ \Rightarrow 10 = 10$
Here, we got the left-hand side equal to the right-hand side.
So, we get the correct value of x is 4.