Question

How do you solve \[9x = 27?\]

Answer 1

Hint:The given problem involves the arithmetic operation of addition/ subtraction/ multiplication/ division. Also, we need to know how to find the greatest common factor between two numbers. To Solve the given equation we need to find the value of \[x\]. Also, we need to know how to convert the fraction into the whole number term.

Complete step by step solution:
The given question is shown below,
\[9x = 27 \to \left( 1 \right)\]
To solve the above equation we have to find the greatest common factor for \[9\]and\[27\].\[9\] can be divided by\[1,3,9\]. \[27\] can be divided by \[1,3,9,27\]. So, the greatest common factor is \[9\].
So, we would divide the equation \[\left( 1 \right)\]by\[9\]. So, we get
\[\left( 1 \right) \to 9x = 27\]
\[\dfrac{{9x}}{9} = \dfrac{{27}}{9} \to \left( 2 \right)\]
We know that,
\[\dfrac{9}{9} = 1\]
So, the equation\[\left( 2 \right)\] becomes,
\[x = \dfrac{{27}}{9}\]
The above equation can also be written as,
\[x = 3\]
So, the final answer is,
\[x = 3\]

Note: The given question can also be solved by moving the term \[9\] from the left side to the right side of the equation. So, we get \[x = \dfrac{{27}}{9}\] it also can be written as \[x = 3\]. So, note that when we move a term from the left side to the right side of the equation the arithmetic operations can be converted as follows,
1) The multiplication process can be converted into a division process.
2) The division process can be converted into a division process.
3) The addition process can be converted into a subtraction process.
4) The subtraction process can be converted into a division process.
We can check the final answer by substituting the \[x\] value in the given equation in the question. If the equation is verified we can confirm that our answer is correct.