Question

Solve the following for the value of x $\dfrac{9x}{7-6x}=15$
$\begin{align}
  & A)x=\dfrac{23}{18} \\
 & B)x=\dfrac{35}{33} \\
 & C)x=\dfrac{5}{3} \\
\end{align}$
$D)x=\dfrac{7}{13}$

Answer 1

Hint: To solve this question for calculating the value of the variable $x$ use the concept of linear equations whereby we simplify the terms to obtain the value of the unknown variable.
The term is given in division therefore we can cross multiply it to the left to get a simplified equation which makes it easy to calculate the value of the variable $x$.

Complete step by step solution:
To simplify the expression $\dfrac{9x}{7-6x}=15$ and calculate the value of the variable x from it.
Writing the equation such that we transfer the denominator to the right hand side, we get:
$\begin{align}
  & \dfrac{9x}{7-6x}=15 \\
 & \Rightarrow 9x=15\left( 7-6x \right) \\
\end{align}$
Now multiply the term 15 to both the terms in the bracket we get,
$9x=15\times 7-15\times 6x$
$\Rightarrow 9x=105-90x$
Using the above equations bring all the terms containing $x$ to one side:
$99x=105$
From the equation find the value of x, we get:
$\Rightarrow x=\dfrac{105}{99}$
Eliminate the common term 3 from numerator and denominator, we get:
$x=\dfrac{35}{33}$
Thus, the correct value of x on solving the expression $\dfrac{9x}{7-6x}=15$ is $x=\dfrac{35}{33}$.

Note: This question can also be solved by first eliminating the term 3 from left-hand side and right-hand side and then the equation that we get is:
$\dfrac{3x}{7-6x}=5$
The equation can now be solved by the same way as mentioned above, that is by cross multiplying the denominator to the right-hand side and then taking all the terms containing x to one side to get the value of x.
Here we must multiply 5 to both the terms of the denominator only then we can find the correct value of x on solving the expression mentioned above.