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Chapter 4: Q. 85 (page 243)

Write a rational inequality whose solution set is ${x ∣ - 3 < x \leq 5}$ .

Short Answer

Expert verified

The rational inequality is $- \frac{3}{5} < \frac{x}{5} \leq 1$ .

Step by step solution

01

Given information

The given solution set is ${x ∣ - 3 < x \leq 5}$ .

02

Determine the rational inequality

Divide by 5 in the given solution set of the inequality.

$- \frac{3}{5} < \frac{x}{5} \leq \frac{5}{5} - \frac{3}{5} < \frac{x}{5} \leq 1$

03

Write the conclusion

The inequality is $- \frac{3}{5} < \frac{x}{5} \leq 1$ .

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Most popular questions from this chapter

Solve the given inequality algebraically.

$x^{3} > 1$

A can in the shape of a right circular cylinder is required to have a volume of $500$ cubic centimeters. The top and bottom are made of material that costs $0.06 ₡$ per square centimeter, while the sides are made of material that costs $0.04 ₡$ per square centimeter.

Part (a) Express the total cost C of the material as a function of the radius r of the cylinder.

Part (b): Graph $C = C (r)$ . For what value of r is the cost C a minimum?

In Problems 63–72, find the real solutions of each equation.

$3 x^{3} - x^{2} - 15 x + 5 = 0$

In Problems 39–56, find the real zeros of f. Use the real zeros to factor f.

$f (x) = 4 x^{5} - 8 x^{4} - x + 2$

In Problems 13–24, find the domain of each rational function.

$R (x) = \frac{3 (x^{2} - x - 6)}{4 (x^{2} - 9)}$

See all solutions

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