Question

solve the following equation​

Answer 1

$\frac{ - 2x + 1}{3} = 5 - \frac{3(x + 4)}{2} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \frac{ - 2x + 1}{3} + \frac{3(x + 4)}{2} = 5 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \frac{2( - 2x + 1) + 3 (3x + 12)}{3 \times 2} = 5 \\ \\ \frac{ - 4x + 2 + 9x + 36}{6} = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \frac{5x + 38}{6} = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ 5x + 38 = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ 5x = 30 - 38 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ x = \frac{ - 8}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

I hope this will be help you

Answer 2

Question

$\sf \large \dfrac{ - 2x + 1}{3} = 5 - \dfrac{3(x + 4)}{2}$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{ - 2x + 1}{ 3} = 5 - \dfrac{3(x + 4)}{2}$

$\sf \longmapsto \dfrac{ - 2x + 1}{3} = \dfrac{10 - 3(x + 4)}{2}$

$\sf \longmapsto \dfrac{ - 2x + 1}{3} = \dfrac{10 - 3x - 12}{2}$

$\sf \longmapsto \dfrac{ - 2x + 1}{3} = \dfrac{ - 2 - 3x}{2}$

Now,cross multiply to both sides:

$\sf \longmapsto2( - 2x + 1) = 3( - 2 - 3x)$

$\sf \longmapsto - 4x + 2 = - 6 - 9x$

$\sf \longmapsto - 4x + 9x = - 6 - 2$

$\sf \longmapsto5x = - 8$

$\sf \longmapsto \: x = \dfrac{ - 8}{5}$

$\sf \bold{x = - \dfrac{8}{5} }$

Check

$\sf \longmapsto2( - 2x + 1) = 3( - 2 - 3x)$

Taking LHS

$\sf \large\longmapsto2( - 2 \times - \frac{8}{5} + 1)$

$\sf \large\longmapsto2( \frac{ 16}{5} + 1)$

$\sf\large \longmapsto2( \frac{16 + 5}{5} )$

$\sf\large \longmapsto2( \frac{21}{5} )$

$\sf = \dfrac{42}{5}$

Taking RHS

$\sf\large \longmapsto3( - 2 - 3 \times - \frac{8}{5} )$

$\sf \large\longmapsto3( - 2 + \frac{24}{5} )$

$\sf \large\longmapsto3( \frac{ - 10 + 24}{5} )$

$\sf\large \longmapsto3( \frac{14}{5} )$

$\sf = \dfrac{42}{5}$

Since,LHS=RHS (verified)