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Chapter 1: Problem 90

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

Define the two inequalities

An absolute value inequality splits into two separate inequalities. In this case, the inequality \(4<|2-x|\) splits into \(2-x< -4\) and \(2-x > 4\).
02

Solve the first inequality

Solving for \( x \) in the inequality \(2-x< -4\) gives \(x > 6\).
03

Solve the second inequality

Solving for \( x \) in the inequality \(2-x > 4\) gives \(x < -2\).
04

Write the final solution

For \(4<|2-x|\), \( x \) must be less than -2 or greater than 6.

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