Question

Solve \[4\left( {2 - x} \right) = 8\]

Answer 1

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

Complete step by step solution:
The given question is shown below,
 \[4\left( {2 - x} \right) = 8\]
The above equation can also be written as,
 \[8 - 4x = 8 \to \left( 1 \right)\]
To solve the above equation we have to find the greatest common factor between \[8\& 4\] . The number \[8\] can be divided by \[1,2,4,8\] and the number \[4\] can be divided by \[1,2,4\] . So, the greatest common factor of \[8\& 4\] is \[4\] .
So, we would divide the equation \[\left( 1 \right)\] by \[4\] . So, we get
 \[\left( 1 \right) \to 8 - 4x = 8\]
 \[\dfrac{8}{4} - \dfrac{4}{4}x = \dfrac{8}{4}\] \[ \to \left( 2 \right)\]
We know that,
 \[\dfrac{8}{4} = 2\] And \[\dfrac{4}{4} = 1\]
So, the equation \[\left( 2 \right)\] becomes,
 \[\left( 2 \right) \to \dfrac{8}{4} - \dfrac{4}{4}x = \dfrac{8}{4}\]
 \[2 - x = 2\]
The above equation can also be written as,
 \[2 - 2 = x\]
So, we get
 \[x = 0\]
So, the final answer is,
 \[x = 0\]

Note: The given question describes the arithmetic operations like addition/ subtraction/ multiplication/ division. Note that when we move the term from LHS to RHS or RHS to LHS, the arithmetic operations can be modified as follow,
The addition process can be converted into a subtraction process.
The subtraction process can be converted into an additional process.
The multiplication process can be converted into a division process.
The division process can be converted into a multiplication process.
Also, note that we won’t take \[1\] it as the greatest common factor. Note that the denominator term would not be equal to zero. If the denominator term is zero the value of the term is undefined or infinity.