Question

Find the solution of
(a) 8
(b) -8
(c) 4
(d) None of these

Answer 1

Answer:

answer is (a) that is 8

in the image

Answer 2

Given :

$\boxed{\bf\dfrac{x+6}{4}+\dfrac{x-3}{5}=\dfrac{5x-4}{8}}$

To Find :

The value of x.

Solution :

Analysis :

Here we have use the required identities and evaluate as per the signs to find the value of x.

Explanation :

$\\ :\implies\sf\dfrac{x+6}{4}+\dfrac{x-3}{5}=\dfrac{5x-4}{8}$

Taking LCM of 4 and 5 = 20,

Dividing the denominator with the LCM and multiplying the numerator with the quotient of the numerator,

$\\ :\implies\sf\dfrac{5(x+6)+4(x-3)}{20}=\dfrac{5x-4}{8}$

Expanding the brackets,

$\\ :\implies\sf\dfrac{5x+30+4x-12}{20}=\dfrac{5x-4}{8}$

Arranging the variables,

$\\ :\implies\sf\dfrac{5x+4x+30-12}{20}=\dfrac{5x-4}{8}$

After evaluation,

$\\ :\implies\sf\dfrac{9x+18}{20}=\dfrac{5x-4}{8}$

By cross multiplying,

$\\ :\implies\sf8(9x+18)=20(5x-4)$

Expanding the brackets,

$\\ :\implies\sf72x+144=100x-80$

Transposing -80 to LHS and 72x to RHS,

$\\ :\implies\sf144+80=100x-72x$

After evaluation,

$\\ :\implies\sf224=28x$

$\\ :\implies\sf\dfrac{224}{28}=x$

$\\ :\implies\sf\cancel{\dfrac{224}{28}}=x$

$\\ :\implies\sf8=x$

$\\ \therefore\boxed{\bf x=8.}$

Your answer is option (a).

The value of x is 8.

Verification :

LHS :

• Putting x = 8,

$\\ :\implies\sf\dfrac{x+6}{4}+\dfrac{x-3}{5}$

$\\ :\implies\sf\dfrac{8+6}{4}+\dfrac{8-3}{5}$

$\\ :\implies\sf\dfrac{14}{4}+\dfrac{5}{5}$

$\\ :\implies\sf\dfrac{5(14)+4(5)}{20}$

$\\ :\implies\sf\dfrac{70+20}{20}$

$\\ :\implies\sf\dfrac{90}{20}$

$\\ :\implies\sf\dfrac{9\not{0}}{2\not{0}}$

$\\ :\implies\sf\dfrac{9}{2}$

$\\ \therefore\boxed{\bf LHS=\dfrac{9}{2}.}$

RHS :

• Putting x = 8,

$\\ :\implies\sf\dfrac{5x-4}{8}$

$\\ :\implies\sf\dfrac{5(8)-4}{8}$

$\\ :\implies\sf\dfrac{(5\times8)-4}{8}$

$\\ :\implies\sf\dfrac{40-4}{8}$

$\\ :\implies\sf\dfrac{36}{8}$

$\\ :\implies\sf\dfrac{\cancel{36}\ \ ^9}{\not{8}\ \ ^2}$

$\\ :\implies\sf\dfrac{9}{2}$

$\\ \therefore\boxed{\bf RHS=\dfrac{9}{2}.}$

LHS = RHS.

• Hence verified.