Question

If $\dfrac{5x-7}{3}+2 = \dfrac{4x-3}{4}+4x$ then the value of (8x+5)?
9
13
6
7

Answer 1

Answer:

$:\implies\sf \dfrac{5x-7}{3}+2 = \dfrac{4x-3}{4}+4x\\\\\\:\implies\sf \dfrac{5x-7 + (3 \times 2)}{3} = \dfrac{4x-3 + (4x \times 4)}{4}\\\\\\:\implies\sf \dfrac{5x-7 + 6}{3} = \dfrac{4x-3 + 16x}{4}\\\\\\:\implies\sf \dfrac{5x-1}{3} = \dfrac{20x-3}{4}\\\\\\:\implies\sf (5x - 1) \times 4 = 3 \times (20x - 3)\\\\\\:\implies\sf 20x - 4 = 60x - 9\\\\\\:\implies\sf 9 - 4 = 60x - 20x\\\\\\:\implies\sf 5 = 40x\\\\\\:\implies\sf \dfrac{5}{40} = x\\\\\\:\implies\sf x = \dfrac{1}{8}$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\dashrightarrow\sf 8x+5\\\\\\\dashrightarrow\sf \bigg(8 \times \dfrac{1}{8} \bigg)+5\\\\\\\dashrightarrow\sf 1 + 5\\\\\\\dashrightarrow\sf 6$

⠀

$\therefore\:\underline{\textsf{Hence, required answer is (c) \textbf{6}}}.$

Answer 2

$\longrightarrow \sf \dfrac{5x-7}{3}+2 = \dfrac{4x-3}{4}+4x$

$\longrightarrow \sf \dfrac{5x - 7 + (3 \times 2)}{3} \ = \ \dfrac{4x-3+(4x \times 4)}{4}$

$\longrightarrow \sf \dfrac{5x-7+6}{3} \ = \ \dfrac{4x-3+16x}{4}$

$\longrightarrow \sf \dfrac{5x-1}{3} \ = \ \dfrac{20x-3}{4}$

$\longrightarrow \sf (5x-1) \times 4 = 3 \times (20x - 3)$

$\longrightarrow \sf 20x - 4 = 60x - 9$

$\longrightarrow \sf 9-4 = 60x - 9$

$\longrightarrow \sf 5 = 40x$

$\longrightarrow \sf x = \dfrac{5}{40}$

$\longrightarrow \sf x = \dfrac{1}{8}$

Now,

In the question we are asked to find the value of (8x + 5) = ?

$\longrightarrow \sf 8x + 5$

$\longrightarrow \bigg(8 \times \dfrac{1}{8} \bigg) + 5$

$\longrightarrow \sf 1 + 5$

$\longrightarrow \sf 6$

$\therefore \bf If \dfrac{5x-7}{3}+2 = \dfrac{4x-3}{4}+4x \ then \ the \\ \bf value \ of \ (8x+5) \ is \ 6$