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Chapter 0: Problem 87

Solve each absolute value inequality. $$1<|2-3 x|$$

Short Answer

Expert verified
The solution to the inequality is \(x < 1/3\) and \(x > 1\).

Step by step solution

01

Breakdown absolute value inequality

Break the absolute value inequality \(1<|2-3x|\) into two separate inequalities based on the positive and negative possible values. This gives: \(1< 2-3x\) and \(1< - (2 - 3x)\).
02

Solve first inequality

Solve the first inequality: Subtract \(2\) from both sides, which gives \(-1 < -3x\). Dividing both sides by \(-3\), and remembering to flip the inequality symbol when dividing by a negative number, gives \(x < 1/3\).
03

Solve second inequality

Solve the second inequality: Simplify to get \(1< 3x - 2\). Add \(2\) to both sides, which gives \(3 < 3x\). Then divide by \(3\), getting \(x > 1\).
04

Combine solutions

Combine these two solutions to create the final interval solution. \(x > 1\) and \(x < 1/3\). Remember that inequalities don't include the endpoint, so use parentheses.

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Most popular questions from this chapter

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