Question

Solve the given equation
 $ \dfrac{2x-\left( 7-5x \right)}{9x-\left( 3+4x \right)}=\dfrac{7}{6} $

Answer 1

Hint: Apply the “-“ sign inside the bracket and then simplify the numerator, denominator. Then apply cross multiplication to get with terms of x on both sides of the equation. Try to manipulate and bring x terms to the left hand side. Now find the coefficient of x and divide with it on both sides, by this you get the value of x. The value of x is required to result in this question.

Complete step-by-step answer:
Given in the question, is written in the form of:
 $ \dfrac{2x-\left( 7-5x \right)}{9x-\left( 3+4x \right)}=\dfrac{7}{6} $
By taking cross multiplication, we can write equation as
\[6\left( 2x\text{ }\left( 7\text{ }\text{ }5x \right) \right)\text{ }=\text{ }7\left( 9x\text{ }\text{ }\left( 3\text{ }+\text{ }4x \right) \right)\]
By taking “-“ inside bracket the left hand side will turn in to
\[6\left( 2x\text{ }\text{ }7\text{ }+\text{ }5x \right)\text{ }=\text{ }7\left( 9x\text{ }\text{ }\left( 3\text{ }+\text{ }4x \right) \right)\]
By taking “-“ inside bracket the right hand side, will turn as
\[6\left( 2x\text{ }\text{ }7\text{ }+\text{ }5x \right)\text{ }=\text{ }7\left( 9x\text{ }\text{ }3\text{ }\text{ }4x \right)\]
By grouping similar terms together, we get it as follows
\[6\left( 2x\text{ }+\text{ }5x\text{ }\text{ }7 \right)\text{ }=\text{ }7\left( 9x\text{ }\text{ }4x\text{ }\text{ }3 \right)\]
By taking x as common, we can write the equation as
\[6\left( \left( 2\text{ }+\text{ }5 \right)x\text{ }\text{ }7 \right)\text{ }=\text{ }7\left( \left( 9\text{ }\text{ }4 \right)x\text{ }\text{ }3 \right)\]
By simplifying above equation, we can write it in the form
\[6\left( 7x\text{ }\text{ }7 \right)\text{ }=\text{ }7\left( 5x\text{ }\text{ }3 \right)\]
By multiplying with 6 inside, we can write left hand side
 \[42x-42=7\left( 5x-3 \right)\]
By multiplying with 7 inside, we can write right hand side
\[42x\text{ }\text{ }42\text{ }=\text{ }35x\text{ }\text{ }21\]
By adding 42 on both sides of equation, we can write it as
\[42x\text{ }\text{ }42\text{ }+\text{ }42\text{ }=\text{ }35x\text{ }\text{ }21\text{ }+\text{ }42\]
By cancelling common terms, we can write the equation as
\[42x\text{ }=\text{ }35x\text{ }\text{ }21\text{ }+\text{ }42\]
By taking x as common on left hand side, we can write it as
\[\left( 42\text{ }\text{ }35 \right)\text{ }x\text{ }=\text{ }42\text{ }\text{ }21\]
By simplifying on left hand side, we get it in form of
\[7x\text{ }=\text{ }42\text{ }\text{ }21\]
By simplifying on right hand side, we get it in form of
\[7x\text{ }=\text{ }21\]
By dividing with 7 on both sides, we get it as
 $ x=\dfrac{21}{7} $
By simplifying, we get the value of x as
\[x\text{ }=\text{ }3\]

Note: Be careful while taking the ‘-‘ sign inside even if you miss to change the -5x as +5x whole solution will go wrong. So, do every step carefully, while multiplying 7 inside students forget to multiply it with 3 in a hurry so look at it. Alternately you can form all terms with x on the right hand side and constant to left. Anyways you will get the same result of x.