Question

Find \[x:x = \dfrac{4}{5}\left( {x + 10} \right)\].

Answer 1

Hint: This is a basic linear equation having one variable i.e. x. Here we have to find the value of x. We just need to separate the constants and variables with the help of simple mathematical computation and then we will get our answer.

Complete step-by-step answer:
In this given problem,
We have to solve the given polynomial equation \[x:x = \dfrac{4}{5}\left( {x + 10} \right)\]
Now, \[5\] is a denominator when it crosses “=” it becomes a numerator.
\[5x = 4\left( {x + 10} \right)\]
\[5x = 4x + 40\]
By multiplying \[x + 10\] by \[4\]
\[5x - 4x = 40\]
\[4x\]is positive when it crosses “=” it becomes negative i.e., \[ - 4x\], by solving we get
\[x = 40\]
Hence, the value of x is \[40\].

Note: 1) Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of\[x\] , bring the variable to either left hand side or right hand side and bring all the remaining values(numbers) to the opposite side.
 2) When the numbers or variable crosses the “=” it will take the complete opposite form
i.e., if its numerator it will become a denominator when it crosses the boundary(=). Some examples are given as follows.
Example 1: \[4x = 5\], in this expression \[4\]is the numerator while solving it will become a denominator like this \[x = \dfrac{5}{4}\].
If its denominator it will become a numerator when it crosses the boundary.
Example 2: \[5 = \dfrac{x}{8}\],here \[8\] is the denominator while solving it will become numerator \[5 \times 8 = x\]
Therefore \[x = 40\].
In other words we can say that a number in numerator is in multiplication and a number in denominator is in division.
If it's associated with + then it will be associated with – when it crosses the boundary.
Example 3: \[15 + x = 30\], here 15 is in addition when it crosses it will become subtraction.
\[
  x = 30 - 15 \\
  x = 15 \\
 \]
If it's associated with – then it will be associated with + when it crosses the boundary.
Example 4: \[x - 2 = 3\],here 2 is in subtraction i.e., \[ - 2\] when it crosses boundary it will become \[ + 2\]
\[
  x = 3 + 2 \\
  x = 5 \\
 \]