Question

How do you solve \[2d+\dfrac{1}{5}=\dfrac{3}{5}\]?

Answer 1

Hint: This question is from the linear equation. In this question, first we will take all the constants or fractions to the right side of the equation to get the balanced equation in the form of a linear equation. The general form of the linear equation is x=C, where x is any variable and C is the constant. After that, we will add the constants or fractions. After adding the fractions, we will simplify the further equation, and then we will get the value of d.

Complete step by step answer:
Let us solve this question.
We have to solve the equation \[2d+\dfrac{1}{5}=\dfrac{3}{5}\] which is given in the question or we can say that we have to find d from the equation \[2d+\dfrac{1}{5}=\dfrac{3}{5}\].
The equation which we have to solve is
\[2d+\dfrac{1}{5}=\dfrac{3}{5}\]
After subtracting \[\dfrac{1}{5}\] on both sides of the above equation, we can write the above equation as
\[\Rightarrow 2d+\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{3}{5}-\dfrac{1}{5}\]
The above equation can also be written as
\[\Rightarrow 2d=\dfrac{3}{5}-\dfrac{1}{5}\]
As we can see on the right side of the equation, we can subtract them easily because the numbers in the denominator are the same which is 5.
So, the above equation can be written as
\[\Rightarrow 2d=\dfrac{3-1}{5}\]
\[\Rightarrow 2d=\dfrac{2}{5}\]
Dividing 2 on both sides of the equation, we get
\[\Rightarrow 2d\times \dfrac{1}{2}=\dfrac{2}{5}\times \dfrac{1}{2}\]
After cancelling the number 2 from the denominator and numerator on both sides of equation, we get
\[\Rightarrow d=\dfrac{1}{5}\]

Hence, after solving the equation \[2d+\dfrac{1}{5}=\dfrac{3}{5}\], we get the value of d as \[\dfrac{1}{5}\].

Note: As we can see that this question is from the linear equations, so we should have a better knowledge in that topic. For solving this type of question, we should know how to add or subtract fractions. If we want to check if we are correct or not, then we can cross check the equation.
In the equation \[2d+\dfrac{1}{5}=\dfrac{3}{5}\], we will put the value of d as \[\dfrac{1}{5}\].
\[\Rightarrow 2\left( \dfrac{1}{5} \right)+\dfrac{1}{5}=\dfrac{3}{5}\]
In the left side of equation, we will add \[2\left( \dfrac{1}{5} \right)+\dfrac{1}{5}\], we get
\[\Rightarrow \dfrac{2+1}{5}=\dfrac{3}{5}\]
\[\Rightarrow \dfrac{3}{5}=\dfrac{3}{5}\]
Hence, the value of d that we have found is correct.