Answer
466.5k+ views
Hint: In the above given question, the linear equation is to be solved. It can be solved through many ways, one of them is shown below. Another way to solve the same equation can also be possible by evaluating both the LHS as well as the RHS separately and then equating the final results so obtained.
We have the given equation in the question as,
\[m - \dfrac{{m - 1}}{2} = 1 - \dfrac{{m - 2}}{3}\]
Taking LCM on LHS and RHS, we get,
$ \Rightarrow \dfrac{{2m - m + 1}}{2} = \dfrac{{3 - m + 2}}{3}$
\[ \Rightarrow \dfrac{{m + 1}}{2} = \dfrac{{5 - m}}{3}\]
By cross-multiplication, we get,
\[ \Rightarrow 3(m + 1) = 2(5 - m)\]
\[ \Rightarrow 3m + 3 = 10 - 2m\]
By transposing 3 to RHS and $ - 2m$ to LHS, we get the following equation,
\[ \Rightarrow 3m + 2m = 10 - 3\;\]
\[ \Rightarrow 5m = 7\]
\[ \Rightarrow m = \dfrac{7}{5}\]
Hence, the solution is$(c){\text{ }}m = \dfrac{7}{5}$.
Note: Whenever we face such types of problems the key point is to have a good grasp of the handling of the linear equations. We have to equate both LHS and RHS terms. Various steps may be involved in this calculation including taking LCM, transposition and cross multiplication. In the end, the value of the variable, for which all the calculations were made, will be obtained.
We have the given equation in the question as,
\[m - \dfrac{{m - 1}}{2} = 1 - \dfrac{{m - 2}}{3}\]
Taking LCM on LHS and RHS, we get,
$ \Rightarrow \dfrac{{2m - m + 1}}{2} = \dfrac{{3 - m + 2}}{3}$
\[ \Rightarrow \dfrac{{m + 1}}{2} = \dfrac{{5 - m}}{3}\]
By cross-multiplication, we get,
\[ \Rightarrow 3(m + 1) = 2(5 - m)\]
\[ \Rightarrow 3m + 3 = 10 - 2m\]
By transposing 3 to RHS and $ - 2m$ to LHS, we get the following equation,
\[ \Rightarrow 3m + 2m = 10 - 3\;\]
\[ \Rightarrow 5m = 7\]
\[ \Rightarrow m = \dfrac{7}{5}\]
Hence, the solution is$(c){\text{ }}m = \dfrac{7}{5}$.
Note: Whenever we face such types of problems the key point is to have a good grasp of the handling of the linear equations. We have to equate both LHS and RHS terms. Various steps may be involved in this calculation including taking LCM, transposition and cross multiplication. In the end, the value of the variable, for which all the calculations were made, will be obtained.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)