Question

3(x-1)/16 - 5(x-4)/12 = 2(x-6)/5 + 5/48

Answer 1

★ Answer -

• The value of x = 6.

★ To find -

• The value of x.

★ Step-by-step explanation -

$\Rightarrow\sf \dfrac{3 (x\! - \!1)}{16} \! - \!\dfrac{5 (x \!- \!4)}{12} = \dfrac{2 (x \!-\! 6)}{5} \!+ \! \dfrac{5}{48}$

$\Rightarrow\sf \dfrac{3x \!-\! 3}{16} \!- \! \dfrac{5x \!-\! 20}{12} = \dfrac{2x\! - \!12}{5} \!+\! \dfrac{5}{48}$

$\! \Rightarrow \sf \dfrac{(3x \!- \!3) (3) \!-\! (5x \!-\! 20) (4)}{48} = \dfrac{2x \!- \!12}{5} \!+\! \dfrac{5}{48}$

$\Rightarrow \sf \dfrac{(9x \!- \!9)\! -\! (20x \!-\! 80)}{48} = \dfrac{2x\! - \!12}{5}\! + \! \dfrac{5}{48}$

$\sf \Rightarrow \dfrac{(9x \!-\! 9) \!-\! (20x \!- \!80)}{48} = \dfrac{(2x \!-\! 12) (48) \!+\! (5) (5)}{240}$

$\Rightarrow \sf\dfrac{(9x \!- \!9)\! -\! (20x \!-\! 80)}{48} = \dfrac{96x\! - \!576\! +\! 25}{240}$

$\Rightarrow \sf \dfrac{ - 11x \!+ \!71}{48} = \dfrac{96x\! - \!551}{240}$

$\Rightarrow \sf( - 11x \!+\! 71) (240) = (96x\! - \!551) (48)$

$\Rightarrow\sf - 2640x \! + \! 17040 = 4608x \!- \!26448$

$\Rightarrow\sf - 2640x \!- \!4608x = - 26448\! - \!17040$

$\Rightarrow \sf- 7248x = -43488$

$\Rightarrow \sf x = \cancel{\dfrac{ - 43488}{ \: \: - 7248}}$

$\Rightarrow\underline{\boxed{ \sf x = 6}} \: \bigstar$

Thus -

• The value of x is 6.

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Answer 2

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$\huge\purple{\mathbb{Question:}}$

$\frac{3(x-1)}{16}$ - $\frac{5(x-4)}{12}$ = $\frac{2(x-6)}{5}$ + $\frac{5}{48}$

$\large\green{\underline{{\boxed{\textbf{To\:Find}}}}}$

ㅤㅤㅤㅤㅤㅤ x = ?

$\huge\boxed{\mathfrak{Solution :}}$

ㅤ$\frac{3(x-1)}{16}$ - $\frac{5(x-4)}{12}$ = $\frac{2(x-6)}{5}$ + $\frac{5}{48}$

ㅤ$\frac{3x-3}{16}$ - $\frac{5x-20}{12}$ = $\frac{2x-12}{5}$ + $\frac{5}{48}$

ㅤ$\frac{(3x-3)(3)-(5x-20)(4)}{48}$ = $\frac{2x-12}{5}$ + $\frac{5}{48}$

ㅤ$\frac{(9x-9)-(20x-80)}{48}$ = $\frac{(2x-12)(48)+(5)(5)}{240}$

ㅤ$\frac{(9x-9)-(20x-80)}{48}$ = $\frac{96x - 576 + 25}{240}$

ㅤ$\frac{-11x+71}{48}$ = $\frac{96x-551}{240}$

ㅤ(-11x + 71)(240) = (96x - 551)(48)

ㅤ-2640x + 17040 = 4608x - 26448

ㅤ-2640x - 4608x = -26448 - 17040

ㅤ-7248x = -43448

ㅤx = ${\cancel{\frac{-43448}{-7248}}}$

ㅤㅤㅤ x = 6

Therefore , the value of x is 6.

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