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Chapter 0: Problem 58

Solve each absolute value inequality. $$|x|<5$$

Short Answer

Expert verified
The solution to the inequality |x|<5 is -5<x<5.

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from zero on the number line. No matter if this number is positive or negative, the absolute value is always positive or zero. In our case, |x|<5 means all x that are less than 5 units away from 0.
02

Solve the Inequality

Because the distance between x and 0 needs to be less than 5, x can be any number between -5 and 5. Hence we write -5<x<5.
03

Check the Solution

Take any number between -5 and 5 (let's say 0) and plug it into our inequality. So, |0|<5 which simplifies to 0<5. This inequality is true, hence our solution -5<x<5 is correct.

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A truck can be rented from Basic Rental for \(\$ 50\) per day plus \(\$ 0.20\) per mile. Continental charges \(\$ 20\) per day plus \(\$ 0.50\) per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Basic Rental a better deal than Continental's?

What is a rational expression?

Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells personalized stationery. The weekly fixed cost is \(\$ 3000\) and it costs \(\$ 3,00\) to produce cach package of stationery. The selling price is \(\$ 5.50\) per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?
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