Answer

Verified

390k+ views

**Hint:**In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘x’ terms one side and constants on the other side of the equation.

**Complete step by step solution:**

Given, \[\dfrac{{x + 3}}{2} + \dfrac{{2x}}{7} = 7\].

We first simplify the left hand side of the equation by taking LCM,

\[\dfrac{{7\left( {x + 3} \right) + 2\left( {2x} \right)}}{{14}} = 7\]

Expanding the brackets,

\[\dfrac{{7x + 21 + 4x}}{{14}} = 7\]

Adding the like terms,

\[\dfrac{{11x + 21}}{{14}} = 7\]

We transpose ‘14’ which is present in the left hand side of the equation to the right hand side of the equation by multiplying ‘14’ on the right hand side of the equation.

\[11x + 21 = 7 \times 14\]

\[11x + 21 = 98\]

We transpose 21 to the right hand side of the equation by subtracting 21 on the right hand side of the equation.

\[11x = 98 - 21\]

\[11x = 77\]

We transpose 11 to the right hand side by dividing 11 on the right hand side of the equation we have,

\[x = \dfrac{{77}}{{11}}\]

**\[ \Rightarrow x = 7\] This is the required answer.**

**Note:**We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.

\[\dfrac{{7 + 3}}{2} + \dfrac{{2(7)}}{7} = 7\]

\[\dfrac{{10}}{2} + \dfrac{{14}}{7} = 7\]

\[5 + 2 = 7\]

\[ \Rightarrow 7 = 7\]

Hence the obtained answer is correct.

If we want to transpose a positive number to the other side of the equation we subtract the same number on that side (vice versa). Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.

Recently Updated Pages

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

Advantages and disadvantages of science

A Paragraph on Pollution in about 100-150 Words

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE

10 examples of law on inertia in our daily life

Write a letter to the principal requesting him to grant class 10 english CBSE