Question

Find the value of the unknown variables.
please tell me these questions (e),and (f) step by step like I take the picture of the questions like that you can answer me ​

Answer 1

e))

Given :

$\boxed{\bf\dfrac{a+7}{2}+\dfrac{3a}{5}=1}$

To Find :

The value of a.

Solution :

Analysis :

Using suitable identities and evaluating as per the signs we can find the value of a.

Explanation :

$\\ :\implies\sf\dfrac{a+7}{2}+\dfrac{3a}{5}=1$

Taking LCM of 5 and 2 = 10,

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

$\\ :\implies\sf\dfrac{5(a+7)+2(3a)}{10}=1$

Expanding the brackets,

$\\ :\implies\sf\dfrac{5a+35+6a}{10}=1$

After evaluation,

$\\ :\implies\sf\dfrac{11a+35}{10}=1$

By cross multiplying,

$\\ :\implies\sf11a+35=1\times10$

$\\ :\implies\sf11a+35=10$

Transposing 35 to RHS,

$\\ :\implies\sf11a=10-35$

$\\ :\implies\sf11a=-25$

$\\ :\implies\sf a=\dfrac{-25}{\ \ \ 11}$

$\\ \therefore\boxed{\bf a=\dfrac{-25}{\ \ \ 11}.}$

The value of a is -25/11.

Verification :

RHS :

$\\ :\implies\sf\dfrac{\frac{-25}{\ \ \ 11}+7}{2}+\dfrac{3\times\frac{-25}{\ \ \ 11}}{5}$

$\\ :\implies\sf\dfrac{\frac{-25+77}{11}}{2}+\dfrac{\frac{-75}{\ \ \ 11}}{5}$

$\\ :\implies\sf\dfrac{\frac{52}{11}}{2}+\dfrac{\frac{-75}{\ \ \ 11}}{5}$

$\\ :\implies\sf\left(\dfrac{52}{11}\times\dfrac{1}{2}\right)+\left(\dfrac{-75}{\ \ \ 11}\times\dfrac{1}{5}\right)$

$\\ :\implies\sf\left(\dfrac{\cancel{52}\ \ ^{26}}{11}\times\dfrac{1}{\not{2}}\right)+\left(\dfrac{\cancel{-75}\ \ ^{-15}}{\ \ \ 11}\times\dfrac{1}{\not{5}}\right)$

$\\ :\implies\sf\left(\dfrac{26}{11}\times\dfrac{1}{1}\right)+\left(\dfrac{-15}{\ \ \ 11}\times\dfrac{1}{1}\right)$

$\\ :\implies\sf\dfrac{26}{11}+\dfrac{-15}{\ \ \ 11}=1$

$\\ :\implies\sf\dfrac{26+(-15)}{11}$

$\\ :\implies\sf\dfrac{26-15)}{11}$

$\\ :\implies\sf\dfrac{11}{11}$

$\\ :\implies\sf\cancel{\dfrac{11}{11}}$

$\\ \therefore\boxed{\bf1.}$

RHS :

$\\ \therefore\boxed{\bf1.}$

LHS = RHS.

• Hence verified.

______________________________________

f))

Given :

$\boxed{\bf\dfrac{3a+2}{5}=5}$

To Find :

The value of a.

Solution :

Analysis :

Using suitable identities and evaluating as per the signs we can find the value of a.

Explanation :

$\\ :\implies\sf\dfrac{3a+2}{5}=5$

By cross multiplying,

$\\ :\implies\sf3a+2=5\times5$

$\\ :\implies\sf3a+2=25$

Transposing 2 to RHS,

$\\ :\implies\sf3a=25-2$

$\\ :\implies\sf3a=23$

$\\ :\implies\sf a=\dfrac{23}{3}$

$\\ \therefore\boxed{\bf a=\dfrac{23}{3}.}$

The value of a is 23/5.

Verification :

LHS :

$\\ :\implies\sf\dfrac{3\times\frac{23}{3}+2}{5}$

$\\ :\implies\sf\dfrac{\not{3}\times\frac{23}{\not{3}}+2}{5}$

$\\ :\implies\sf\dfrac{23+2}{5}$

$\\ :\implies\sf\dfrac{25}{5}$

$\\ :\implies\sf\cancel{\dfrac{25}{5}}$

$\\ \therefore\boxed{\bf5.}$

RHS :

$\\ \therefore\boxed{\bf5.}$

LHS = RHS.

• Hence verified.