Chapter 2: Q 2.109 (page 177)

Solve the inequality $\frac{1}{4} x - \frac{1}{12} x > \frac{1}{6} x + \frac{7}{8}$ , graph the solution on the number line, and write the solution in interval notation .

Short Answer

Expert verified

There is no solution of the inequality $\frac{1}{4} x - \frac{1}{12} > \frac{1}{6} x + \frac{7}{8}$

The graph of the solution is :-

Step by step solution

Step 1. Given information

We have given the following inequality :-

$\frac{1}{4} x - \frac{1}{12} x > \frac{1}{6} x + \frac{7}{8}$ .

We have to solve the inequality for values of $x$ .

We will be apply some arithmetic operations, that will convert the quality to a inequality from which we easily determine the interval of solution.

Step 2. Solving the inequality

Multiply both sides of inequality by LCD $24$ , to clear the fraction. Then we have :-

$24 (\frac{1}{4} x - \frac{1}{12} x) > 24 (\frac{1}{6} x + \frac{7}{8}) \Rightarrow 6 x - 2 x > 4 x + 21 \Rightarrow 4 x > 4 x + 21$

Subtract $4 x$ from both sides, then we have :-

$4 x - 4 x > 4 x + 21 - 4 x \Rightarrow 0 > 21$

Step 3. Final Conclusion

As we find $0 > 21$ .

This is a contraction.

So that we can conclude that given inequality has no solution.

The solution graph is as following :-

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Solve the inequality $\frac{1}{4} x - \frac{1}{12} x > \frac{1}{6} x + \frac{7}{8}$ , graph the solution on the number line, and write the solution in interval notation .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the inequality

Step 3. Final Conclusion

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Solve the inequality14x-112x>16x+78, graph the solution on the number line, and write the solution in interval notation .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the inequality

Step 3. Final Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve the inequality $\frac{1}{4} x - \frac{1}{12} x > \frac{1}{6} x + \frac{7}{8}$ , graph the solution on the number line, and write the solution in interval notation .