Q79. Solve the inequality x-2x<x-4... [FREE SOLUTION]

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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:

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

Further simplifying,

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

Step 3. Verify the result for obtained value.

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

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

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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91影视

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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91影视

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

Pure Maths

Discrete Mathematics

Applied Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

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