Question

Solve the expression $\dfrac{9x}{7-6x}=15$ for x.
(a) $\dfrac{99}{105}$
(b) $-\dfrac{105}{99}$
(c) $\dfrac{105}{99}$
(d) $-\dfrac{99}{105}$

Answer 1

Hint: We will take the help of multiplication for this question. Because of this we will multiply n to both sides of the expression of the form $\dfrac{m}{n}=p$ to get m = pn. With this trick the solution will be proceeded easily.

Complete step-by-step answer:
Now we will consider the expression $\dfrac{9x}{7-6x}=15...(i)$.
We will multiply both the sides of the equation by the term $7-6x$. Therefore, we will get $\left( 7-6x \right)\times \dfrac{9x}{7-6x}=\left( 7-6x \right)\times 15$.
After multiplying 15 to the expression $\left( 7-6x \right)$ we will get $9x=\left( 7\times 15 \right)-\left( 6x\times 15 \right)$.
On further solving this equation we lead to a new expression which is written as $9x=105-90x$.
Now we will take all the terms to the right side of the equation. Therefore we get $105-90x-9x=0$.
As we know that – 90x – 9x results into – 99x. Thus we get $105-99x=0$.
Now we will take – 99x to the right side of the equation. That is $105=+99x$.
By dividing both the sides of the equation by 99x we get $x=\dfrac{105}{99}$ which clearly represents the required value of x. This fraction will become 1.0606060606 or $\dfrac{35}{33}$ when simplified further.
Hence the correct option is (c).

Note: With the step $\dfrac{9x}{7-6x}=15...(i)$, we will be able to verify whether our value is right or wrong. This is done as if the value of x satisfies the equation (i) then it will make the left hand side of it equal to 15. If the value of x does not satisfy the expression (i) then the left hand side of the expression will not be equal to 15. We will take care of the fact that the cross multiplication here is done as $\dfrac{a}{b}=\dfrac{c}{d}$ by writing it ad = cb. Therefore, we have $\dfrac{9x}{7-6x}=\dfrac{15}{1}$ as
$\begin{align}
  & 9x=15\left( 7-6x \right) \\
 & \Rightarrow 9x=105-90x \\
\end{align}$