Question

Solve 1/2 (x-6) - 2/5 (x+3) = 7/10​

Answer 1

GIVEN :-

$\\ \sf \: \dfrac{x - 6}{2} - \dfrac{2(x + 3)}{5} = \dfrac{7}{10}$

TO FIND :-

• Value of x.

SOLUTION :-

We have,

$\\ \implies \sf \: \dfrac{x - 6}{2} - \dfrac{2(x + 3)}{5} = \dfrac{7}{10} \\ \\ \implies\sf \: \dfrac{5(x - 6) - 2 \{2(x + 3) \}}{10} = \dfrac{7}{10} \\ \\ \implies\sf \: \dfrac{5x - 30 - 4(x + 3)}{10} = \dfrac{7}{10} \\ \\ \implies\sf \: \dfrac{5x - 30 - 4x - 12}{10} = \dfrac{7}{10}$

$\implies\sf \: \dfrac{x - 42}{10} = \dfrac{7}{10} \\ \\ \implies\sf \: x - 42 = \dfrac{7}{ \cancel{10}} \times \cancel{10} \\ \\ \implies\sf \: x - 42 = 7 \\ \\ \implies\sf \: x = 7 + 42 \\ \\ \implies \boxed{ \boxed{\sf \: x = 49}}$

Hence , x = 49.

VERIFICATION :-

$\\ \longmapsto\sf \: \dfrac{49 - 6}{2} - \dfrac{2(49 + 3)}{5} = \dfrac{7}{10} \\ \\ \longmapsto\sf \: \dfrac{43}{2} - \dfrac{2(52)}{5} = \dfrac{7}{10} \\ \\ \longmapsto\sf \: \dfrac{43}{2} - \dfrac{104}{5} = \dfrac{7}{10}$

$\longmapsto\sf \: \dfrac{43(5) - 104(2)}{10} = \dfrac{7}{10} \\ \\ \longmapsto\sf \: \dfrac{215 - 208}{10} = \dfrac{7}{10} \\ \\ \longmapsto\sf \: \dfrac{7}{10} = \dfrac{7}{10} (verified)$