Question

5/7(3a-2)=3/4(a+1)+2/3a​

Answer 1

Step-by-step explanation:

$\frac{5}{7(3a - 2)} = \frac{3}{4(a + 1)} + \frac{2}{3a}$

$\frac{5}{21a - 14} = \frac{3}{4a + 4} + \frac{2}{3a}$

$\frac{5}{21a - 14} = \frac{9a + 8a + 8}{12 {a}^{2} + 12a}$

$\frac{5}{21a - 14} = \frac{17a + 8}{12 {a}^{2} + 12a}$

HOPE IT HELPS U...

Answer 2

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

$\sf \dfrac{5}{7} (3a - 2) = \dfrac{3}{4} (a + 1) + \dfrac{2}{3} a$

$\sf \longmapsto \dfrac{15a - 10}{7} = \dfrac{3a + 3}{4} + \dfrac{2}{3} a$

$\sf \longmapsto \dfrac{15a - 10}{7} = \dfrac{3(3a + 3) + 4(2a)}{12}$

$\sf \longmapsto \dfrac{15a - 10}{7} = \dfrac{9a + 9 + 8a}{12}$

$\sf \longmapsto \dfrac{15a - 10}{7} = \dfrac{17a + 9}{12}$

$\sf \longmapsto12(15a - 10) = 7(17a + 9)$

$\sf \longmapsto180a - 120 = 119a + 63$

$\sf \longmapsto180a - 119a = 63 + 120$

$\sf \longmapsto61a = 183$

$\sf \longmapsto \: a = \dfrac{183}{63} = 3$

$\sf \large\bold{{\red{a = 3}}}$

Check

$\sf \longmapsto \dfrac{15a - 10}{7} = \dfrac{3[3a + 3) + 4(2a)]}{12}$

$\sf \longmapsto \dfrac{15 \times 3 - 10}{7} = \dfrac{3[3 \times 3 + 3 + 4(6)]}{12}$

$\sf \longmapsto \dfrac{45 - 10}{7} = \dfrac{3(12) + 24}{12}$

$\sf \longmapsto \dfrac{35}{7} = \dfrac{36 + 24}{12} = \dfrac{60}{12}$

$\sf \longmapsto \dfrac{35}{7} = \dfrac{60}{12}$

$\sf \longmapsto5 = 5$