Answer

Verified

339.6k+ 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

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

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

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

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE