Chapter 2: Q 2.110 (page 177)

Solve the inequality $\frac{2}{5} z - \frac{1}{3} z < \frac{1}{15} z - \frac{3}{5}$ , graph the solution on the number line, and write the solution in interval notation.

Short Answer

Expert verified

There is no solution of the given inequality $\frac{2}{5} z - \frac{1}{3} z < \frac{1}{15} z - \frac{3}{5}$ .

Step by step solution

Step 1. Given information

We have given the following inequality :-

$\frac{2}{5} z - \frac{1}{3} z < \frac{1}{15} z - \frac{3}{5}$ .

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.

z-z<z-z-9⇒0<-9Step 2. Solve the inequality

Multiply both sides with LCD 15, to clear the fractions, then we have :-

$15 (\frac{2}{5} z - \frac{1}{3} z) < 15 (\frac{1}{15} z - \frac{3}{5}) \Rightarrow 6 z - 5 z < z - 9 \Rightarrow z < z - 9$

Now subtract $z$ from both sides, then we have :-

$z - z < z - z - 9 \Rightarrow 0 < - 9$

This is a contraction.

Step 3. Conclusion

As there is a contraction while solving the inequality.

So that the given inequality is not true.

Hence we can conclude that the given inequality hasno solution.

We can draw the solution graph as following :-

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Solve the inequality $\frac{2}{5} z - \frac{1}{3} z < \frac{1}{15} z - \frac{3}{5}$ , graph the solution on the number line, and write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Given information

z-z<z-z-9⇒0<-9Step 2. Solve the inequality

Step 3. Conclusion

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Solve the inequality 25z-13z<115z-35, graph the solution on the number line, and write the solution in interval notation.

Short Answer

Step by step solution

Step 1. Given information

z-z<z-z-9⇒0<-9Step 2. Solve the inequality

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the inequality $\frac{2}{5} z - \frac{1}{3} z < \frac{1}{15} z - \frac{3}{5}$ , graph the solution on the number line, and write the solution in interval notation.