Question

(5y-4)/6 + (3y+10)/2 = 4y+1 Solve the following linear equation and Verify the solution.

Answer 1

Solution :

$\underline{\bf{Given\::}}}}$

$\sf{\dfrac{(5y-4)}{6} +\dfrac{(3y+10)}{2} =4y+1}$

$\underline{\bf{Explanation\::}}}}$

$\longrightarrow\sf{\dfrac{(5y-4)}{6} +\dfrac{(3y+10)}{2} =4y+1}\\\\\\\longrightarrow\sf{\dfrac{(5y-4)+(9y+30)}{6} =4y+1\:\:\: \bigg[\therefore taking\:L.C.M\:of\:6\:\&\:2\bigg]}\\\\\\\longrightarrow\sf{\dfrac{5y-4+9y+30}{6}=4y+1}\\\\\\\longrightarrow\sf{5y-4+9y+30=6(4y+1)}\\\\\longrightarrow\sf{14y+26=24y+6}\\\\\longrightarrow\sf{14y-24y=6-26}\\\\\longrightarrow\sf{-10y=-20}\\\\\longrightarrow\sf{y=\cancel{-20/-10}}\\\\\longrightarrow\bf{y=2}$

$\boxed{\bf{V\:\:E\:\:R\:\:I\:\:F\:\:I\:\:C\:\:A\:\:T\:\:I\:\:O\:\:N}}}$

Putting the value of y in the given equation to both side,we get;

$\longrightarrow\sf{\dfrac{5\times 2-4}{6} +\dfrac{3\times 2+10}{2} =4\times 2+1}\\\\\\\longrightarrow\sf{\dfrac{10-4}{6} +\dfrac{6+10}{2} =8+1}\\\\\\\longrightarrow\sf{\cancel{\dfrac{6}{6}} +\cancel{\dfrac{16}{2} }=9}\\\\\\\longrightarrow\sf{1+8=9}\\\\\longrightarrow\bf{9=9}$

Thus,

Verified .

Answer 2

Solution :

\sf{\dfrac{(5y-4)}{6} +\dfrac{(3y+10)}{2} =4y+1}

6

(5y−4)

+

2

(3y+10)

=4y+1

\begin{lgathered}\longrightarrow\sf{\dfrac{(5y-4)}{6} +\dfrac{(3y+10)}{2} =4y+1}\\\\\\\longrightarrow\sf{\dfrac{(5y-4)+(9y+30)}{6} =4y+1\:\:\: \bigg[\therefore taking\:L.C.M\:of\:6\:\&\:2\bigg]}\\\\\\\longrightarrow\sf{\dfrac{5y-4+9y+30}{6}=4y+1}\\\\\\\longrightarrow\sf{5y-4+9y+30=6(4y+1)}\\\\\longrightarrow\sf{14y+26=24y+6}\\\\\longrightarrow\sf{14y-24y=6-26}\\\\\longrightarrow\sf{-10y=-20}\\\\\longrightarrow\sf{y=\cancel{-20/-10}}\\\\\longrightarrow\bf{y=2}\end{lgathered}

⟶

6

(5y−4)

+

2

(3y+10)

=4y+1

⟶

6

(5y−4)+(9y+30)

=4y+1[∴takingL.C.Mof6&2]

⟶

6

5y−4+9y+30

=4y+1

⟶5y−4+9y+30=6(4y+1)

⟶14y+26=24y+6

⟶14y−24y=6−26

⟶−10y=−20

⟶y=

−20/−10

⟶y=2

Putting the value of y in the given equation to both side,we get;

\begin{lgathered}\longrightarrow\sf{\dfrac{5\times 2-4}{6} +\dfrac{3\times 2+10}{2} =4\times 2+1}\\\\\\\longrightarrow\sf{\dfrac{10-4}{6} +\dfrac{6+10}{2} =8+1}\\\\\\\longrightarrow\sf{\cancel{\dfrac{6}{6}} +\cancel{\dfrac{16}{2} }=9}\\\\\\\longrightarrow\sf{1+8=9}\\\\\longrightarrow\bf{9=9}\end{lgathered}

⟶

6

5×2−4

+

2

3×2+10

=4×2+1

⟶

6

10−4

+

2

6+10

=8+1

⟶

6

6

+

2

16

=9

⟶1+8=9

⟶9=9

Thus,

Verified .

Hope this helps you