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Chapter 0: Problem 51

Solve each compound inequality. $$-3 \leq x-2<1$$

Short Answer

Expert verified
The solution to the compound inequality \(-3 \leq x-2<1\) is \(-1 \leq x < 3\).

Step by step solution

01

Solving the first inequality

First, focus on the inequality \(-3 \leq x-2\). The goal is to isolate \(x\) here. To do this, add 2 on both sides of the inequality to balance. The result is \(-1 \leq x\).
02

Solving the second inequality

Next, consider the inequality \(x-2<1\). Again, isolating \(x\) requires adding 2 on both sides, which results in \(x <3\).
03

Finding the shared solution

The solution for \(x\) must satisfy both inequalities. Therefore, the final values that \(x\) can take are those that are greater than or equal to -1 but less than 3.

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Most popular questions from this chapter

Describe how to solve an absolute value inequality involving the symbol <. Give an example.

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

Describe two ways to simplify \(\frac{\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x^{2}}+\frac{2}{x}}\).

Will help you prepare for the material covered in the first section of the next chapter. If \(y=|x+1|,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -4 and ending with 2

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although I can solve \(3 x+\frac{1}{5}=\frac{1}{4}\) by first subtracting \(\frac{1}{5}\) from both sides, I find it easier to begin by multiplying both sides by \(20,\) the least common denominator.
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