Question

If for a particular value of the variable \(x\), the following holds good \(17=\frac {17x}{(1-x)}\), then compute the value of \((2x)x\).

• A. 17
• B. 1
• C. 2
• D. \(\frac 12\)

Answer 1

The Correct Option is D

Given the equation \(17=\frac{17x}{1-x}\), let's solve for \(x\). First, multiply both sides by \(1-x\) to eliminate the fraction:

\[17(1-x)=17x\]

Expand the equation:

\[17-17x=17x\]

Move \(17x\) from the left to the right side of the equation:

\[17=17x+17x\]

\[17=34x\]

Divide both sides by 34 to solve for \(x\):

\[x=\frac{17}{34}\]

Simplify \(\frac{17}{34}\) to get:

\[x=\frac{1}{2}\]

We need to compute \((2x)x\):

Substitute \(x=\frac{1}{2}\):

\[(2x)x=(2 \times \frac{1}{2}) \times \frac{1}{2}\]

Simplify:

\[=1 \times \frac{1}{2}\]

\[=\frac{1}{2}\]

Thus, the value of \((2x)x\) is \(\frac{1}{2}\).