Question

Solve that:
 $ \dfrac{{4x - \left( {x + 7} \right)}}{{3x - \left( {5x - 9} \right)}} = \dfrac{2}{3} $

Answer 1

Hint: In this particular question use the concept of cross multiplication rule (i.e. numerator of the L.H.S is multiplied by the denominator of the R.H.S and denominator of the L.H.S is multiplied by the numerator of the R.H.S) so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given equation is
 $ \dfrac{{4x - \left( {x + 7} \right)}}{{3x - \left( {5x - 9} \right)}} = \dfrac{2}{3} $
Now we have to solve the above equation for x.
So first simplify the numerator and denominator of the L.H.S part of the above equation we have,
 $ \Rightarrow \dfrac{{4x - x - 7}}{{3x - 5x + 9}} = \dfrac{2}{3} $
 $ \Rightarrow \dfrac{{3x - 7}}{{ - 2x + 9}} = \dfrac{2}{3} $
Now apply cross multiplication rule (i.e. numerator of the L.H.S is multiplied by the denominator of the R.H.S and denominator of the L.H.S is multiplied by the numerator of the R.H.S) so we have,
 $ \Rightarrow 3\left( {3x - 7} \right) = 2\left( { - 2x + 9} \right) $
Now again simplify the above equation we have,
 $ \Rightarrow 3\left( {3x} \right) - 3\left( 7 \right) = 2\left( { - 2x} \right) + 2\left( 9 \right) $
 $ \Rightarrow 9x - 21 = - 4x + 18 $
Now take 4x to the L.H.S side and -21 to the R.H.S side we have,
 $ \Rightarrow 9x + 4x = 18 + 21 $
Now again simplify the above equation we have,
 $ \Rightarrow 13x = 39 $
Now divide by 13 throughout we have,
 $ \Rightarrow x = \dfrac{{39}}{{13}} = 3 $
So this is the required solution of the given equation.
So, x = 3 is the required answer.

Note: Whenever we face such types of question the key concept is simplification of the equation, so first simplify the numerator and denominator of the L.H.S part of the given equation as above, then apply cross multiplication rule which is stated above then again simplify as above we will get the required solution of the given equation.