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Which number line represents the solution to the inequality -14x – 15 > 27? |

Which number line represents the solution to the inequality -14x – 15 > 27? |

Algebra and Trigonometry (6th Edition)
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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Question
**Question:** Which number line represents the solution to the inequality \(-14x - 15 \geq 27\)? **Number Line Options:** - **A** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(-3\), including it (solid dot), extends to the left. - **B** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(3\), not including it (open dot), extends to the left. - **C** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(0\), including it (solid dot), extends to the right. - **D** - Interval shown is from less than \(-10\) to 10. - Arrow starts from \(-3\), including it (solid dot), extends to the right. **Explanation:** To determine which number line represents the solution, solve the given inequality \(-14x - 15 \geq 27\). 1. Add 15 to both sides: \(-14x \geq 42\) 2. Divide by \(-14\), remembering to reverse the inequality sign: \(x \leq -3\) The solution is \(x \leq -3\), which corresponds to option **A**, where the arrow starts from \(-3\) (inclusive) and extends to the left.
Transcribed Image Text:**Question:** Which number line represents the solution to the inequality \(-14x - 15 \geq 27\)? **Number Line Options:** - **A** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(-3\), including it (solid dot), extends to the left. - **B** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(3\), not including it (open dot), extends to the left. - **C** - Interval shown is from less than \(-10\) to 10. - Arrow starting from \(0\), including it (solid dot), extends to the right. - **D** - Interval shown is from less than \(-10\) to 10. - Arrow starts from \(-3\), including it (solid dot), extends to the right. **Explanation:** To determine which number line represents the solution, solve the given inequality \(-14x - 15 \geq 27\). 1. Add 15 to both sides: \(-14x \geq 42\) 2. Divide by \(-14\), remembering to reverse the inequality sign: \(x \leq -3\) The solution is \(x \leq -3\), which corresponds to option **A**, where the arrow starts from \(-3\) (inclusive) and extends to the left.
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