Question

Solve and find the value of x​

Answer 1

Solution!!

$\sf \to \dfrac{2x+7}{5}-\dfrac{3x+11}{2}=\dfrac{2x+8}{3}-5$

Taking the LCM

$\sf \to \dfrac{2(2x+7)-5(3x+11)}{10}=\dfrac{2x+8-15}{3}$

Simplifying the numerators

$\sf \to \dfrac{4x+14-15x-55}{10}=\dfrac{2x-7}{3}$

$\sf \to \dfrac{-11x-41}{10}=\dfrac{2x-7}{3}$

Cross multiplication

$\sf \to 3(-11x-41)=10(2x-7)$

Simplification

$\sf \to -33x-123=20x-70$

$\sf \to -33x-20x=123-70$

$\sf \to -53x = 53$

$\sf \to x = \dfrac{53}{-53}$

$\sf \to \boxed{\bold{x=-1}}$

Verification:-

Taking LHS

$\sf \to \dfrac{2x+7}{5}-\dfrac{3x+11}{2}$

$\sf \to \dfrac{2(-1)+7}{5}-\dfrac{3(-1)+11}{2}$

$\sf \to \dfrac{-2+7}{5}-\dfrac{-3+11}{2}$

$\sf \to \dfrac{5}{5}-\dfrac{8}{2}$

$\sf \to \dfrac{10-40}{10}$

$\sf \to \dfrac{-30}{10}$

$\sf \to \bold{-3}$

Taking RHS

$\sf \to \dfrac{2x+8}{3}-5$

$\sf \to \dfrac{2(-1)+8}{3}-5$

$\sf \to \dfrac{-2+8}{3}-5$

$\sf \to \dfrac{6}{3}-5$

$\sf \to \dfrac{6-15}{3}$

$\sf \to \dfrac{-9}{3}$

$\sf \to \bold{-3}$

LHS = RHS

Hence, verified.

Answer 2

-3 is the correct answer and thank u