# Chapter 2 - Section 2.7 - Linear Inequalities and Problem Solving - Exercise Set: 85

The direction of the inequality symbol is reversed when you multiply or divide an inequality by a negative number.

#### Work Step by Step

Take the inequality: $5 \lt 20$ as an eample. When multiplying the inequality by $-1$, $-5 \lt -20$. This is false as -5 should be greater than -20. So this is only true when the inequality sign is reversed. $-5 \gt -20$ A larger magnitude of a positive value is larger than a smaller magnitude of a positive value. However, a smaller magnitude of a negative value is larger than a larger magnitude of a negative value. Hence, the inequality sign is reversed when multiplying or dividing by a negative value. See "question 84" as another example.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-2-section-2-7-linear-inequalities-and-problem-solving-exercise-set-page-173/85", "fetch_time": 1524382444000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2018-17/segments/1524125945497.22/warc/CC-MAIN-20180422061121-20180422081121-00376.warc.gz", "warc_record_offset": 434615702, "warc_record_length": 14408, "token_count": 216, "char_count": 935, "score": 4.25, "int_score": 4, "crawl": "CC-MAIN-2018-17", "snapshot_type": "latest", "language": "en", "language_score": 0.8781405091285706, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00026-of-00064.parquet"}