Solve the following equations and verify your answer - 2x-7 - 5x-9x-3-4x - 7-6

2x (7 5x)/9x (3+4x) = 7/6⇒2x 7+5x/9x 3 4x = 7/6 ⇒7x 7/5x 3 = 7/6 By cross multiplication : 6(7x 7) = 7(5x 3) ⇒ 42x 42=35x 21 ⇒ 42x 35x = 21 + 42 ⇒ 7x = 21 ⇒ ...

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Standard VIII

Mathematics

Equations Reducible to the Linear Form

Solve the fol...

Question

Solve the following equations and verify your answer :

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

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Solution

$\frac{2 x - (7 - 5 x)}{9 x - (3 + 4 x)} = \frac{7}{6} \Rightarrow \frac{2 x - 7 + 5 x}{9 x - 3 - 4 x} = \frac{7}{6} \Rightarrow \frac{7 x - 7}{5 x - 3} = \frac{7}{6}$
By cross multiplication :
$6 (7 x - 7) = 7 (5 x - 3) \Rightarrow 42 x - 42 = 35 x - 21 \Rightarrow 42 x - 35 x = - 21 + 42 \Rightarrow 7 x = 21 \Rightarrow x = \frac{21}{7} = 3 ∴ x = 3$
Verification :
$L . H . S . = \frac{2 x - (7 - 5 x)}{9 x - (3 + 4 x)} = \frac{2 \times 3 - (7 - 5 \times 3)}{9 \times 3 - (3 + 4 \times 3)} = \frac{6 - (7 - 15)}{27 - (3 + 12)} = \frac{6 - 7 + 15}{27 - 3 - 12} = \frac{14}{12}$
$= \frac{7}{6}$ = R.H.S.

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Solve the following equations and verify your answer : 2x−(7−5x)9x−(3+4x)=76

Solve the following equations and verify your answer :

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