Question

a - (3a - (2a - 5)/10) - (2a - 57)/6 = - 5/3​

Answer 1

Question:

Find the value of a.

$\displaystyle{\sf\:a\:-\:\left(\:3a\:-\:\dfrac{2a\:-\:5}{10}\:\right)\:-\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)\:=\:-\:\dfrac{5}{3}}$

Answer:

The value of a is 5.

Step-by-step-explanation:

The given equation is

$\displaystyle{\sf\:a\:-\:\left(\:3a\:-\:\dfrac{2a\:-\:5}{10}\:\right)\:-\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)\:=\:-\:\dfrac{5}{3}}$

We have to find the value of a.

Now,

$\displaystyle{\sf\:a\:-\:\left(\:3a\:-\:\dfrac{2a\:-\:5}{10}\:\right)\:-\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)\:=\:-\:\dfrac{5}{3}}$

$\displaystyle{\implies\sf\:a\:-\:\left(\:\dfrac{30a\:-\:(\:2a\:-\:5\:)}{10}\:\right)\:=\:\dfrac{-\:5}{3}\:+\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)}$

$\displaystyle{\implies\sf\:a\:-\:\left(\:\dfrac{30a\:-\:2a\:+\:5}{10}\:\right)\:=\:\dfrac{-\:5\:\times\:2}{3\:\times\:2}\:+\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)}$

$\displaystyle{\implies\sf\:a\:-\:\left(\:\dfrac{28a\:+\:5}{10}\:\right)\:=\:\dfrac{-\:10}{6}\:+\:\left(\:\dfrac{2a\:-\:57}{6}\:\right)}$

$\displaystyle{\implies\sf\:a\:-\:\left(\:\dfrac{28a\:+\:5}{10}\:\right)\:=\:\dfrac{-\:10}{6}\:+\:\dfrac{2a\:-\:57}{6}}$

$\displaystyle{\implies\sf\:a\:-\:\left(\:\dfrac{28a\:+\:5}{10}\:\right)\:=\:\dfrac{-\:10\:+\:2a\:-\:57}{6}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{2a\:-\:10\:-\:57}{6}\:+\:\left(\:\dfrac{28a\:+\:5}{10}\:\right)}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{2a\:-\:67}{6}\:+\:\dfrac{28a\:+\:5}{10}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{10\:(\:2a\:-\:67\:)\:+\:6\:(\:28a\:+\:5\:)}{6\:\times\:10}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{\cancel{2}\:[\:5\:(\:2a\:-\:67\:)\:+\:3\:(\:28a\:+\:5\:)\:]}{\cancel{6}\:\times\:10}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{10a\:-\:335\:+\:84a\:+\:15}{3\:\times\:10}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{10a\:+\:84a\:-\:335\:+\:15}{30}}$

$\displaystyle{\implies\sf\:30a\:=\:94a\:-\:320}$

$\displaystyle{\implies\sf\:94a\:-\:30a\:=\:320}$

$\displaystyle{\implies\sf\:64a\:=\:320}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{\cancel{320}}{\cancel{64}}}$

$\displaystyle{\implies\sf\:a\:=\:\cancel{\dfrac{40}{8}}}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:a\:=\:5\:}}}}$

∴ The value of a is 5.

Answer 2

$\large\underline{ \underline{ \text{Question:}}}$

• $a - \bigg [3a - \frac{2a - 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\large\underline{ \underline{ \text{Solution:}}}$

Given,

• $a - \bigg [3a - \frac{2a - 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

It should done as,

$\implies a - \bigg [3a - \frac{2a - 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\implies a - \bigg [ \frac{3a(10) - 2a - 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\implies a - \bigg [ \frac{30a - (2a - 5)}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\implies a - \bigg [ \frac{30a - 2a + 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\implies a - \bigg [ \frac{28a + 5}{10} \bigg ] - \bigg[ \frac{2a - 57}{6} \bigg] = - \frac{5}{3}$

$\implies a - \frac{28a + 5}{10} - \frac{2a - 57}{6} = - \frac{5}{3}$

$\implies \frac{30(a) - 3(28a + 5) - 5(2a - 57)}{30} = - \frac{5}{3}$

$\implies \frac{30a - 84a - 15 - 10a + 285}{30} = - \frac{5}{3}$

$\implies \frac{- 64a + 270}{30} = - \frac{5}{3}$

$\implies - 64a + 270 = - \frac{5}{3} \times 30$

$\implies - 64a + 270 = - 5 \times 10$

$\implies - 64a + 270 = - 50$

$\implies - 64a = - 50 - 270$

$\implies - 64a = - 320$

$\implies a = \frac{ - 320}{ - 64}$

$\implies a = \frac{ \cancel{- 64} \times 5}{ \cancel{- 64}}$

$\implies \boxed{ a = 5}$

$\large\underline{ \underline{ \text{Required Answer:}}}$

• The value of a is 5.