Question

How do you write the expression for “twice the difference of the number Z and 12 is equal to 10”?

Answer 1

Hint:Difference is also known as the subtraction. When the number is multiplied by 2 then it is said to be twice that number. Form the expression from the statement solves for Z using the transposition method.

Complete Step by Step Solution:
In the question, the statement is given which is twice the difference of the number Z and 12 is equal to 10. There are two terms given in the question which are twice and different. So, first, we should understand both the terms one by one.
Twice the number can be defined as the number with which the 2 is multiplied with that number. When the number 2 is multiplied with the number then, the newly formed number is said to be twice that previous number.
The difference between the number is said to be the subtraction between two numbers. For example, when the two numbers are subtracted then it is said to be the difference between two numbers.
So, in the question, there is written that there is a difference between the number Z and 12. Hence, it can be written as –
$ \Rightarrow Z - 12$
It is also written that twice the difference between the number Z and 12. So, in the equation form, it can be written that –
$ \Rightarrow 2\left( {Z - 12} \right)$
This equation is equal to 10.
$\therefore 2\left( {Z - 12} \right) = 10$
Solving this equation by using the transposition method, we get –
$
   \Rightarrow Z - 12 = 5 \\
   \Rightarrow Z = 17 \\
 $

Hence, the value of Z is 17.

Note: This formed equation can also be solved by using the cross – multiplication method. So, the equation can be written as –
$\dfrac{{Z - 12}}{1} = \dfrac{{10}}{2}$.
In this method, the denominator is multiplied with the numerator of another fraction, and the numerator is multiplied with the denominator of another fraction. Then, we will also get the value of Z equal to 17.