Solve the following equations and verify your answer:

$\frac{15(2-x)-5(x+6)}{1-3 x}=10 $

Given: $\frac{15( 2\ -\ x) \ -\ 5( x\ +\ 6)}{1\ -\ 3x} \ =\ 10$   ....(i)

To find: Value of $x$.

Solution:

Given that:

$ \begin{array}{l}
\frac{15( 2\ -\ x) \ -\ 5( x\ +\ 6)}{1\ -\ 3x} \ =\ 10\\
\\
\\
\\
15( 2\ -\ x) \ -\ 5( x\ +\ 6) \ =\ 10( 1\ -\ 3x)\\
\\
\\
\\
30\ -\ 15x\ -\ 5x\ -\ 30\ =\ 10\ -\ 30x\\
\\
\\
\\
-\ 20x\ =\ 10\ -\ 30x\\
\\
\\
\\
30x\ -\ 20x\ =\ 10\\
\\
\\
\\
10x\ =\ 10\\
\\
\\
\mathbf{x\ =\ 1}
\end{array}$

Now, putting this value of $x$ in eq (i):

$ \begin{array}{l}
\frac{15( 2\ -\ x) \ -\ 5( x\ +\ 6)}{1\ -\ 3x} \ =\ 10\\
\\
\\
\\
\frac{15( 2\ -\ 1) \ -\ 5( 1\ +\ 6)}{1\ -\ 3( 1)} \ =\ 10\\
\\
\\
\\
\frac{15( 1) \ -\ 5( 7)}{1\ -\ 3} \ =\ 10\\
\\
\\
\\
\frac{15\ -\ 35}{-\ 2} \ =\ 10\\
\\
\\
\\
\frac{-\ 20}{-\ 2} \ =\ 10\\
\\
\\
\\
\mathbf{10\ =\ 10}
\end{array}$

So, the value of $x = 2$.

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Updated on: 10-Oct-2022

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