Question

please answer now help me
answer is -1 but U don't know how to do???☹️​

Answer 1

${\mathfrak{\underline{\underline{\blue{Answer :-}}}}}$

x = -1

${\mathfrak{\underline{\underline{\red{Step-By-Step-Explanation:-}}}}}$

To Find :-

$\bf{\frac{2x + 3}{3x + 4} = \frac{2x - 3}{3x - 2}}$

➭ Let this be equation 1

Solution :-

By cross multiplication method

$\sf{ 3x - 2(2x + 3) = 3x + 4(2x - 3)}$

$\sf{6 {x}^{2} + 9x - 4x - 6 = 6 {x}^{2} - 9 x +8 x - 12}$

$\sf{{\cancel6x^{2} } \: + 5x - 6 = { \cancel6 {x}^{2} } - x - 12}$

$\sf {5x + x = - 12 + 6}$

$\sf{6x = -6}$

$\sf{x = \frac{{ {\blue{\cancel - 6}}}}{{{\blue{ \cancel6}}}}}$

$\large{\boxed{\underline{\red{x = -1}}}}$

$\rule{200}{2}$

Verification :-

_________________[Put values]

$\sf{ \frac{2( - 1) + 3}{3( - 1) + 4} = \frac{2( - 1) - 3}{3( - 1) - 2} }$

$\sf{ \frac{ - 2 + 3}{ - 3 + 4} = \frac{ - 2 - 3}{ - 3 - 2}}$

$\sf{ \frac{ 1}{1} = \frac{{ {\orange{\cancel - 5}}}}{{{\orange{\cancel - 5}}}} }$

$\bf{1 = 1}$

L. H. S = R. H. S

Hence proved

Answer 2

Question :-

Solve (2x + 3)/(3x + 4) = (2x - 3)/(3x - 2) and verify the answer.

Answer :-

$\sf \dfrac{2x + 3}{3x + 4} = \dfrac{2x - 3}{3x - 2}$

By cross multiplication

⇒ (2x + 3)(3x - 2) = (2x - 3)(3x + 4)

⇒ 2x(3x - 2) + 3(3x - 2) = 2x(3x + 4) - 3(3x + 4)

⇒ 6x² - 4x + 9x - 6 = 6x² + 8x - 9x - 12

Adding like terms

⇒ 6x² + 5x - 6 = 6x² - x - 12

⇒ 6x² + 5x - 6x² + x = - 12 + 6

⇒ 6x = - 6

⇒ x = - 6/6

⇒ x = - 1

Verification :-

$\sf \dfrac{2x + 3}{3x + 4} = \dfrac{2x - 3}{3x - 2} \\ \\ \\ \sf \dfrac{2( - 1) + 3}{3( - 1) + 4} = \dfrac{2( - 1) - 3}{3( - 1) - 2} \\ \\ \\ \sf \dfrac{ - 2 + 3}{ - 3 + 4} = \dfrac{ - 2 - 3}{ - 3 - 2} \\ \\ \\ \sf \dfrac{1}{1} = \dfrac{ - 5}{ - 5} \\ \\ \\ \sf 1 = 1 \\ \\ \\ \tt LHS = RHS \\ \\ \\ \bf \underline{ Hence \: verified.}$