Answer
Verified
412.2k+ views
Hint: In order to solve this type of linear equation in one variable, first send all the constants to the right hand side and variables to the left hand side of the equation with the help of algebraic operations and then divide both the sides with the coefficient of the variable to get the desired solution for the equation.
Complete step-by-step answer:
To solve the given equation $ 3x - \dfrac{1}{3} = 5 $ , we will first send all the variables to the left hand side (L.H.S.) of the equation and constants to the right hand side of the equation (R.H.S.), so we can see that in the given equation $ 3x - \dfrac{1}{3} = 5 $ , we have to send only one constant from the left hand side to the right hand side, for this we will add both sides $ \dfrac{1}{3} $ , we will get
$
\Rightarrow 3x - \dfrac{1}{3} = 5 \\
\Rightarrow 3x - \dfrac{1}{3} + \dfrac{1}{3} = 5 + \dfrac{1}{3} \\
\Rightarrow 3x = 5 + \dfrac{1}{3} \;
$
Now taking L.C.M. in order to add \[5\;{\text{and}}\;\dfrac{1}{3}\]
$
\Rightarrow 3x = 5 + \dfrac{1}{3} \\
\Rightarrow 3x = \dfrac{{5 \times 3 + 1}}{3} \\
\Rightarrow 3x = \dfrac{{16}}{3} \;
$
Dividing both sides with the coefficient of $ x $ that is $ 3 $ to get the value for $ x $
$
\Rightarrow 3x = \dfrac{{16}}{3} \\
\Rightarrow \dfrac{{3x}}{3} = \dfrac{{16}}{{3 \times 3}} \\
\Rightarrow x = \dfrac{{16}}{9} \;
$
Therefore $ x = \dfrac{{16}}{9} $ is the required solution for the equation $ 3x - \dfrac{1}{3} = 5 $
So, the correct answer is “ $ x = \dfrac{{16}}{9} $ ”.
Note: The final result is in improper fraction, which means the numerical value of the numerator is greater than the numerical value of the denominator. So either convert the result into mixed fraction or write it in decimal form with the help of long division method.
Complete step-by-step answer:
To solve the given equation $ 3x - \dfrac{1}{3} = 5 $ , we will first send all the variables to the left hand side (L.H.S.) of the equation and constants to the right hand side of the equation (R.H.S.), so we can see that in the given equation $ 3x - \dfrac{1}{3} = 5 $ , we have to send only one constant from the left hand side to the right hand side, for this we will add both sides $ \dfrac{1}{3} $ , we will get
$
\Rightarrow 3x - \dfrac{1}{3} = 5 \\
\Rightarrow 3x - \dfrac{1}{3} + \dfrac{1}{3} = 5 + \dfrac{1}{3} \\
\Rightarrow 3x = 5 + \dfrac{1}{3} \;
$
Now taking L.C.M. in order to add \[5\;{\text{and}}\;\dfrac{1}{3}\]
$
\Rightarrow 3x = 5 + \dfrac{1}{3} \\
\Rightarrow 3x = \dfrac{{5 \times 3 + 1}}{3} \\
\Rightarrow 3x = \dfrac{{16}}{3} \;
$
Dividing both sides with the coefficient of $ x $ that is $ 3 $ to get the value for $ x $
$
\Rightarrow 3x = \dfrac{{16}}{3} \\
\Rightarrow \dfrac{{3x}}{3} = \dfrac{{16}}{{3 \times 3}} \\
\Rightarrow x = \dfrac{{16}}{9} \;
$
Therefore $ x = \dfrac{{16}}{9} $ is the required solution for the equation $ 3x - \dfrac{1}{3} = 5 $
So, the correct answer is “ $ x = \dfrac{{16}}{9} $ ”.
Note: The final result is in improper fraction, which means the numerical value of the numerator is greater than the numerical value of the denominator. So either convert the result into mixed fraction or write it in decimal form with the help of long division method.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE