Solve the following equation and verify your answer:
Question:

Solve the following equation and verify your answer:

$\frac{2 x-(7-5 x)}{9 x-(3+4 x)}=\frac{7}{6}$

Solution:

$\frac{2 x-(7-5 x)}{9 x-(3+4 x)}=\frac{7}{6}$

or $\frac{7 x-7}{5 x-3}=\frac{7}{6}$

or $42 \mathrm{x}-42=35 \mathrm{x}-21$ [After c ross multiplication]

or $42 \mathrm{x}-35 \mathrm{x}=-21+42$

or $7 \mathrm{x}=21$

or $\mathrm{x}=\frac{21}{7}$

or $\mathrm{x}=3$

Thus, $\mathrm{x}=3$ is the solution of the given equation.

Check:

Substituting $x=3$ in the given equation, we get :

L. H.S. $=\frac{2 \times 3-(7-5 \times 3)}{9 \times 3-(3+4 \times 3)}=\frac{6-(7-15)}{27-(3+12)}=\frac{6+8}{27-15}=\frac{14}{12}=\frac{7}{6}$

R.H.S. $=\frac{7}{6}$

$\therefore$ L.H.S. $=$ R.H.S. for $\mathrm{x}=3$.

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