17. Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line. -3(x + 5) > -3 Choose the correct graph below that is the solution set to the inequality. O A. +H -9 В. -6 -3 3 6 9 -9 -6 -3 9 OC. D. -6 -3 3 -9 -6 -3 3 O E. F. -9 -3 3 6 9 -6 -3 3

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem 17.**

Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line.

\[
-3(x + 5) \geq -3
\]

**Solution:**

First, distribute the -3:

\[
-3x - 15 \geq -3
\]

Add 15 to both sides:

\[
-3x \geq 12
\]

Divide both sides by -3 (and remember to flip the inequality sign):

\[
x \leq -4
\]

**Set-builder notation:** \(\{ x \, | \, x \leq -4 \} \)

**Interval notation:** \((-\infty, -4]\)

**Graphs Explanation:**

- **A:** The arrow starts at 5 and points right, open at 5.
- **B:** The arrow starts at -4 and points left, closed at -4.
- **C:** No arrow, open at 5.
- **D:** The arrow starts at -4 and points right, open at -4.
- **E:** A line with arrows at both ends, spanning from -9 to 9.
- **F:** The arrow starts at -4 and points right, closed at -4.

The correct graph is **B**: It visually represents all numbers less than or equal to -4, with a closed circle at -4, and the line extends to the left indicating all smaller numbers.
Transcribed Image Text:**Problem 17.** Solve the inequality. Express the solution set in set-builder notation and interval notation. Graph the solution set on a real number line. \[ -3(x + 5) \geq -3 \] **Solution:** First, distribute the -3: \[ -3x - 15 \geq -3 \] Add 15 to both sides: \[ -3x \geq 12 \] Divide both sides by -3 (and remember to flip the inequality sign): \[ x \leq -4 \] **Set-builder notation:** \(\{ x \, | \, x \leq -4 \} \) **Interval notation:** \((-\infty, -4]\) **Graphs Explanation:** - **A:** The arrow starts at 5 and points right, open at 5. - **B:** The arrow starts at -4 and points left, closed at -4. - **C:** No arrow, open at 5. - **D:** The arrow starts at -4 and points right, open at -4. - **E:** A line with arrows at both ends, spanning from -9 to 9. - **F:** The arrow starts at -4 and points right, closed at -4. The correct graph is **B**: It visually represents all numbers less than or equal to -4, with a closed circle at -4, and the line extends to the left indicating all smaller numbers.
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