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Chapter 0: Problem 88

Solve each absolute value inequality. $$4<|2-x|$$

Short Answer

Expert verified
The solution to the inequality 4 < |2-x| is \(x < -2\) or \(x > 6\).

Step by step solution

01

Understand the Nature of the Absolute Value

The first step is understanding that the absolute value of a quantity indicates its distance from zero, without regard to direction. Therefore, the absolute value inequality |2-x| > 4 can be separated into two separate inequalities.
02

Decouple into Two Inequalities

So the inequality separates into 2-x > 4 and 2-x < -4. Solve each of these inequalities separately.
03

Solve First Inequality

Starting with 2-x > 4, subtract 2 from both sides to obtain -x > 2, and then multiply both sides by -1, which reverses the inequality sign, leading to x < -2.
04

Solve Second Inequality

For 2-x < -4, subtract 2 from both sides to get -x < -6, multiply both sides by -1, which leads to x > 6.

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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 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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