Chapter 10: Q79. (page 530)

Solve the inequality $\frac{x - 2}{x} < \frac{x - 4}{x - 6}$ . Check your solution.

Short Answer

Expert verified

The solution for the given inequality is $0 < x < 3 or x > 6$ .

Step by step solution

Step 1. Write down the given expression.

The given inequality is $\frac{x - 2}{x} < \frac{x - 4}{x - 6}$ .

Step 2. Simplify the equation.

The given inequality $\frac{x - 2}{x} < \frac{x - 4}{x - 6}$ is solved as:

$\begin{array}{l} \frac{x - 2}{x} < \frac{x - 4}{x - 6} .... (Given) \\ \frac{x - 2}{x} - \frac{x - 4}{x - 6} < 0 \\ \frac{(x - 2) (x - 6) - x (x - 4)}{x (x - 6)} < 0 \\ \frac{x^{2} - 8 x + 12 - x^{2} + 4 x}{x (x - 6)} < 0 \\ \frac{- 4 x + 12}{x (x - 6)} < 0 \end{array}$

Further simplifying,

$\begin{array}{l} \frac{- 4 (x - 3)}{x (x - 6)} < 0 \\ \frac{(x - 3)}{x (x - 6)} > 0.... (\begin{array}{l} Divideby - 4 and \\ reversetheinequality \end{array}) \\ 0 < x < 3 or x > 6 \end{array}$

Step 3. Verify the result for obtained value.

Plugging $x > 6$ say $x = 7$ in given inequality and verify the result.

$\begin{array}{l} \frac{x - 2}{x} < \frac{x - 4}{x - 6} .... (Given) \\ \frac{(7) - 2}{(7)} < \frac{(7) - 4}{(7) - 6} .... (Plugging x = 7) \\ \frac{5}{7} < \frac{3}{1} \\ \frac{5}{7} < 3.... (True) \end{array}$

Hence the solution is verified for $x = 7$ .

Step 4. Conclusion.

The solution for the given inequality is $0 < x < 3 or x > 6$ .

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Solve the inequality $\frac{x - 2}{x} < \frac{x - 4}{x - 6}$ . Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

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Solve the inequality x-2x<x-4x-6. Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Solve the inequality $\frac{x - 2}{x} < \frac{x - 4}{x - 6}$ . Check your solution.