If 1-6 -1-7 -x-8 - find x-

1/6!+1/7!=x/8!, ⇒ 1/6!+1/7× 6!=x/8× 7× 6! ⇒ 1/6![1+1/7 ]=1/6![x/8× 7 ] ⇒ 8/7=x/8× 7 ⇒ x=64. ...

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Byju's Answer

Standard XII

Mathematics

Combination

If 1/6 !+1/7 ...

Question

If $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},$ find x.

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Solution

$\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},$

$\Rightarrow \frac{1}{6!} + \frac{1}{7 \times 6!} = \frac{x}{8 \times 7 \times 6!}$

$\Rightarrow \frac{1}{6!} [1 + \frac{1}{7}] = \frac{1}{6!} [\frac{x}{8 \times 7}]$

$\Rightarrow \frac{8}{7} = \frac{x}{8 \times 7} \Rightarrow x = 64.$

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Similar questions

Q. If

\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}

, find

x

Q. If

\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},

find

x .

Q. If

\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}

, then

x =

Find x in each of the following :
(i) $\frac{1}{4!} + \frac{1}{5!} = \frac{x}{6!}$
(ii) $\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$
(iii) $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$

Solve : $\frac{2 x}{3} - \frac{x - 1}{6} + \frac{7 x - 1}{4} = 2 \frac{1}{6} .$

Hence, find the value of 'a', if $\frac{1}{a} + 5 x = 8.$

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If 16!+17!=x8!, find x.

16!+17!=x8!, ⇒ 16!+17×6!=x8×7×6! ⇒ 16![1+17]=16![x8×7] ⇒ 87=x8×7 ⇒ x=64.

If $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},$ find x.

$\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},$

$\Rightarrow \frac{1}{6!} + \frac{1}{7 \times 6!} = \frac{x}{8 \times 7 \times 6!}$

$\Rightarrow \frac{1}{6!} [1 + \frac{1}{7}] = \frac{1}{6!} [\frac{x}{8 \times 7}]$

$\Rightarrow \frac{8}{7} = \frac{x}{8 \times 7} \Rightarrow x = 64.$