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Answer 1

Solution!!

$\sf \to \dfrac{2x}{3}-\dfrac{x-1}{6}+\dfrac{7x-1}{4}=2\dfrac{1}{6}$

Convert into improper fraction.

$\sf \to \dfrac{2x}{3}-\dfrac{x-1}{6}+\dfrac{7x-1}{4}=\dfrac{13}{6}$

Taking the LCM.

$\sf \to \dfrac{4(2x)-2(x-1)+3(7x-1)}{12}=\dfrac{13}{6}$

Taking the denominator to the RHS.

$\sf \to 4(2x)-2(x-1)+3(7x-1)=\dfrac{13}{6}\times 12$

$\sf \to 4(2x)-2(x-1)+3(7x-1)=13\times 2$

$\sf \to 4(2x)-2(x-1)+3(7x-1)=26$

$\sf \to 8x-2x+2+21x-3=26$

$\sf \to 27x-1=26$

$\sf \to 27x=26+1$

$\sf \to 27x=27$

$\sf \to x=\dfrac{\cancel{27}}{\cancel{27}}$

$\boxed{\sf x=1}$

Verification.

Taking LHS

$\sf \to \dfrac{2x}{3}-\dfrac{x-1}{6}+\dfrac{7x-1}{4}$

$\sf \to \dfrac{2x}{3}-\dfrac{x-1}{6}+\dfrac{7x-1}{4}$

$\sf \to \dfrac{2(1)}{3}-\dfrac{1-1}{6}+\dfrac{7(1)-1}{4}$

$\sf \to \dfrac{2}{3}-\dfrac{0}{6}+\dfrac{7-1}{4}$

$\sf \to \dfrac{2}{3}+\dfrac{6}{4}$

$\sf \to \dfrac{4(2)+3(6)}{12}$

$\sf \to \dfrac{8+18}{12}$

$\sf \to \dfrac{26}{12}$

$\sf \to \dfrac{13}{6}$

$\sf \to 2\dfrac{1}{6}$

LHS = RHS

Hence, verified.

Answer 2

Photosynthesis, the process by which green plants and certain other organisms transform light energy into chemical energy. During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy-rich organic compounds.