Solve each of the following equations and verify the result:
(i) $5 (3 x + 4) - 8 (6 x - 7) = 9 x - 8$
(ii) $2 x - \frac{3 x}{5} = 7$

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Solution

$5 (3 x + 4) - 8 (6 x - 7) = 9 x - 8$
$L H S = 5 (2 x + 4) - 8 (6 x - 7)$
$∴ L H S = 15 x + 20 - 48 x + 56$
$∴ L H S = 76 - 33 x$
Now $R H S = 9 x - 8$
$L H S = R H S$
$∴ 76 - 33 x = 9 x - 8$
$∴ 84 = 33 x + 3 x$
$∴ 84 = 42 x$
$∴= \frac{84}{42} = 2$
$∴ x = 2$
Verifying:
Putting $x = 2$ in given equation
$5 (3 \times 2 + 4) - 8 (6 \times 2 - 7) = 9 (2) - 8$
$5 (6 + 4) - 8 (x - 7) = 18 - 8$
$∴ 50 - 40 = 10$
$∴ 10 = 10$
Hence verified
$2 x - \frac{3 x}{5} = 7$
$L H S = 2 x - \frac{3 x}{5}$
$= \frac{10 x - 3 x}{5} = \frac{7 x}{5}$
Now $R H S = 7$
$∴ L H S = R H S$
$∴ \frac{7 x}{5} = 7$
$∴ x = \frac{7 \times 5}{7}$
$∴ x = 5$
Verifying:Putting $x = 5$ in given equation
$2 (5) - \frac{3 (5)}{5} = 7$
$7 = 7$
Hence verified

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Similar questions

Solve:-

(i) $5 (3 x - 4) - 8 (6 x - 7) = 9 x - 8$

(ii) $2 x - \frac{3 x}{5} = 7$

(iii) $\frac{2 z}{3} - 5 = \frac{3 z}{4} - 1$

(iv) $\frac{4 x}{7} - 12 = 7$

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