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How do you solve $x+\dfrac{1}{4}x=30$ ?

Last updated date: 05th Mar 2024
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IVSAT 2024
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Hint: For answering this question we are asked to solve the given equation $x+\dfrac{1}{4}x=30$ and find the value of the variable $x$ . For solving that we will make some transformations like shifting from right hand to left hand side and vice versa and basic arithmetic simplifications like addition and subtraction then we need to conclude the value of the unknown variable $x$

Complete answer:
Now considering from the question we have been asked to solve the given equation $x+\dfrac{1}{4}x=30$ and derive the value of unknown variable $x$ .
Firstly we will observe the given equation and bring all the terms containing the unknown variable $x$ one side and the other terms on the other side of the equation.
If we observe the given equation carefully it is already arranged similarly.
Now by performing basic arithmetic simplifications that is addition in this case we will get the equation reduced to $\Rightarrow \dfrac{5}{4}x=30$ .
Now we will transform the $4$ from the left hand side to the right hand side after this transformation we will have $\Rightarrow 5x=4\times 30$ .
Now we will perform the multiplication arithmetic operation involved in the right hand side of the equation after that we will have $\Rightarrow 5x=120$ .
Now after this we will transform $5$ from the left hand side to the right hand side then we will have $\Rightarrow x=\dfrac{120}{5}$ .
By further performing the division operation for the terms involved in the right hand side we will have $\Rightarrow x=24$ .
Therefore we can conclude that the value of $x$ in $x+\dfrac{1}{4}x=30$ is $24$ .

We should be sure with our calculations while solving this question and the transformations and basic arithmetic simplifications we make. Similarly we can solve the same type of equations for example $p+\dfrac{1}{3}p=4\Rightarrow \dfrac{4}{3}p=4\Rightarrow p=3$ . It’s better to verify the value we got before finalising the answer here verification means substituting the value we got in the equation $x+\dfrac{1}{4}x=30$ in the place of $x$ . As we had got $x=24$ by substituting it in the left hand side we will have,
  & 24+\dfrac{1}{4}\left( 24 \right) \\
 & \Rightarrow 24+6 \\
 & \Rightarrow 30 \\
which is equal to the value in the right hand side.
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