Question

Refer to the Attachment ⬆

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Answer 1

Answer:

Given:

$\dfrac{x-6}{4} - \dfrac{x-4}{6} = 1 - \dfrac{x}{10}$

Solution:

$\implies \dfrac{x - 6}{4} - \dfrac{x-4}{6} = 1 - \dfrac{x}{10}$

$\implies \dfrac{(x-6)6 - (x-4)4}{(6)(4)} = \dfrac{10 - x}{10}$

$\implies \dfrac{6x - 36 - 4x + 16}{24} = \dfrac{10-x}{10}$

$\implies \dfrac{2x - 20}{24} = \dfrac{10-x}{10}$

$\implies \dfrac{x-10}{12} = \dfrac{10 - x}{10}$

$\implies 10(x-10) = 12(10-x)$

$\implies 10x - 100 = 120 - 12x$

$\implies 10x + 12x = 120 + 100$

$\implies 22x = 220$

$\boxed{\implies{\boxed{x = 10}}}$