Question
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Ifst 110 \( -9 \leq x+2<9 \) selve and write interval notation for the solution set. Then graph the solution Isolate \( x \) in the compound inequality. \( -11 \leq x<7 \) (Simplify your answers. Use integers or fractions for any Select the correct choice below and, if necessary, fill in the answer box to the expression.) complete your choice. A. The solution set in interval notation is \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no solution.

Ask by Parry Pearson. in the United States
Feb 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solution set in interval notation is [–11, 7).

Solution

We start with the inequality   –9 ≤ x + 2 < 9 To solve for x, subtract 2 from every part of the inequality:   –9 – 2 ≤ x + 2 – 2 < 9 – 2 This simplifies to:   –11 ≤ x < 7 Thus, the solution set in interval notation is:   [–11, 7) Graphing this on a number line: • Place a closed (filled-in) circle at –11 (indicating that –11 is included). • Place an open circle at 7 (indicating that 7 is not included). • Shade the line between –11 and 7. So the answer is Choice A: The solution set in interval notation is [–11, 7).

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Bonus Knowledge

To solve the compound inequality \( -9 \leq x + 2 < 9 \), we first isolate \( x \) by subtracting 2 from all parts of the inequality. This gives us: \(-9 - 2 \leq x < 9 - 2\) Which simplifies to: \(-11 \leq x < 7\) In interval notation, this solution set is expressed as \([-11, 7)\). When you graph this solution on a number line, you would draw a solid dot at -11 to indicate that -11 is included in the solution (due to the square bracket), and an open dot at 7 to show that 7 is not included (denoted by the parentheses). So, you can fill in the choices: A. The solution set in interval notation is \([-11, 7)\).

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