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Chapter 0: Problem 71

Solve each absolute value inequality. $$|3 x-8|>7$$

Short Answer

Expert verified
The solution to the inequality \( |3x - 8| > 7 \) is \(x > 5 \) OR \( x < \frac{1}{3} \)

Step by step solution

01

Setting Up the Inequalities

An absolute value is a distance, and so it can be either positive or negative. So, set the problem up as two separate inequalities. \(3x - 8 > 7\) and \(3x - 8 < -7\) to account for the possibility that the value within the absolute signs can be negative or positive.
02

Solving First Inequality

Solve the first inequality. Start by adding 8 on both sides to isolate the term with x on one side: \(3x > 15\). Finally, divide by 3 on both sides to solve for x: \(x > 5\).
03

Solving Second Inequality

Similarly, solve the second inequality. Begin by adding 8 on both sides of the second inequality: \(3x < 1\). Then divide by 3 on both sides to get: \(x < \frac{1}{3}\)
04

Interpreting the Result

Since it is an 'or' inequality, the solution involves either of the two ranges. This means the final solution is \(x > 5 \) OR \( x <\frac{1}{3} \)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The model \(P=-0.18 n+2.1\) describes the number of pay phones, \(P,\) in millions, \(n\) years after \(2000,\) so I have to solve a linear equation to determine the number of pay phones in 2010.

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)

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