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Chapter 0: Problem 92

Solve each absolute value inequality. $$\left|2-\frac{x}{2}\right|-1 \leq 1$$

Short Answer

Expert verified
The solution to the absolute value inequality is \(0 \leq x \leq 8\).

Step by step solution

01

Rewrite equality without absolute value

Firstly, the absolute value inequality should be rewritten as the following two separate inequalities: \(2-\frac{x}{2}-1 \leq 1\) and \(-(2-\frac{x}{2}-1) \leq 1\).
02

Simplify inequalities

Next, simplify the inequalities. This should result in the following two inequalities: \(\frac{x}{2} \geq 0\) and \(\frac{x}{2} \leq 4\).
03

Solving for x

Finally, solve for x in each of the resulting inequalities. This would be done by multiplying each side by 2. The solution will be \(x \geq 0\) and \(x \leq 8\).

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Most popular questions from this chapter

The rational expression $$\frac{130 x}{100-x}$$ describes the cost, in millions of dollars, to inoculate \(x\) percent of the population against a particular strain of flu. a. Evaluate the expression for \(x=40, x=80,\) and \(x=90\) Describe the meaning of each evaluation in terms of percentage inoculated and cost. b. For what value of \(x\) is the expression undefined? c. What happens to the cost as \(x\) approaches \(100 \% ?\) How can you interpret this observation?

Explain how to determine which numbers must be excluded from the domain of a rational expression.

What is a compound inequality and how is it solved?

Perform the indicated operations. $$(x-y)^{-1}+(x-y)^{-2}$$

Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.
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