Question

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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Question No 1 :-

$\bigstar\: \: \sf\bold{\purple{a)\: \dfrac{6x + 1}{3} + 1 =\: \dfrac{x - 3}{6}}}$

$\longrightarrow \sf \dfrac{6x + 1}{3} + 1 =\: \dfrac{x - 3}{6}$

$\longrightarrow \sf \dfrac{6x + 1 + 3}{3} =\: \dfrac{x - 3}{6}$

$\longrightarrow \sf \dfrac{6x + 4}{3} =\: \dfrac{x - 3}{6}$

By doing cross multiplication we get,

$\longrightarrow \sf 6(6x + 4) =\: 3(x - 3)$

$\longrightarrow \sf 36x + 24 =\: 3x - 9$

$\longrightarrow \sf 36x - 3x =\: - 9 - 24$

$\longrightarrow \sf 33x =\: - 33$

$\longrightarrow \sf x =\: \dfrac{- \cancel{33}}{\cancel{33}}$

$\longrightarrow \sf x =\: \dfrac{- 1}{1}$

$\longrightarrow \sf\bold{\red{x =\: - 1}}$

${\small{\bold{\underline{\therefore\: The\: value\: of\: x\: is\: - 1\: .}}}}$

Question No 2 :-

$\bigstar\: \: \sf\bold{\purple{b)\: \dfrac{9x - 7}{3x + 5} =\: \dfrac{3x - 4}{x + 6}}}$

$\implies \sf \dfrac{9x - 7}{3x + 5} =\: \dfrac{3x - 4}{x + 6}$

By doing cross multiplication we get,

$\implies \sf (9x - 7)(x + 6) =\: (3x - 4)(3x + 5)$

$\implies \sf 9x^2 + 54x - 7x - 42 =\: 9x^2 + 15x - 12x - 20$

$\implies \sf {\cancel{9x^2}} {\cancel{- 9x^2}} + 54x - 7x - 15x + 12x =\: - 20 + 42$

$\implies \sf 54x - 7x - 15x + 12x =\: - 20 + 42$

$\implies \sf 47x - 15x + 12x =\: 22$

$\implies \sf 47x - 3x =\: 22$

$\implies \sf 44x =\: 22$

$\implies \sf x =\: \dfrac{\cancel{22}}{\cancel{44}}$

$\implies \sf x =\: \dfrac{\cancel{11}}{\cancel{22}}$

$\implies \sf\bold{\red{x =\: \dfrac{1}{2}}}$

${\small{\bold{\underline{\therefore\: The\: value\: of\: x\: is\: \dfrac{1}{2}\: .}}}}$