Question

Linear equations in one variable. solve the equation and verify your result.

Answer 1

$\bold {\huge {Solutions :-}}$

$Q: \frac{3x}{10(2 - x) - 3(x + 2)} = \frac{ - 6}{40} \\ \\ = > \frac{3x}{20 - 10x - 3x - 6} = \frac{ - 3}{20} \\ \\ = > 3x \times 20 = - 3(20 - 10x - 3x - 6) \\ \\ = > 60x = - 60 + 30x + 9x + 18 \\ \\ = > 60x - 30x - 9x = - 60 + 18 \\ \\ = > 21x = - 42 \\ \\ = > x = \frac{ - 42}{21} = - 2$



$\bold {\underline {Now~verification:-}}$

For verification put the value of x in the equation.


$\frac{3 \times - 2}{10(2 - \times - 2) - 3( - 2 + 2)} = \frac{ - 6}{40} \\ \\ = > \frac{3 \times - 2}{20 - 10 \times - 2 - 3 \times - 2 - 6} = \frac{ - 3}{20} \\ \\ = > 3 \times - 2 \times 20 = - 3(20 - 10 \times - 2 \: - 3 \times - 2 - 6) \\ \\ = > 60 \times - 2 = - 60 + 30 \times - 2 + 9 \times - 2 + 18 \\ \\ = > 60 \times - 2 - 30 - 2 - 9 \times - 2 = - 60 + 18 \\ \\ = > 21 \times - 2 = - 42 \\ \\ = > - 2= \frac{ - 42}{21} = - 2$



$\bold {\underline {Hence, }}$

$\bold {L.H.S~ = ~R.H.S~ verified }$

Answer 2

Answer :-

$\frac{3x}{10(2 - x) - 3(x + 2)} = \frac{ - 6}{40}$





$40 \times 3x = - 6(10(2 - x)3(x + 2))$





$120x = - 60(2 - x) + 18(x + 2)$





$120x = - 12 0+ 60x + 18x + 36$





$120x = 78x - 84$





$120x - 78x = - 84$





$42x = - 84$





$x = \frac{ - 84}{42}$





$x = - 2$






Verification:






$\frac{3x}{10(2 - x) - 3(x + 2)} = \frac{ - 6}{40}$





Simplyfying LHS






Putting x = -2






$\frac{3 \times (- 2)}{10(2 - ( - 2)) - 3( - 2 + 2)}$






$\frac{ - 6}{(10 \times 4) - 3(0)}$





$\frac{ - 6}{40 - 0}$
$\frac{ - 6}{40}$






RHS = >






$\frac{ - 6}{40}$






Hence, LHS = RHS







Hence verified.