Algebra
Topics

# How do you solve 80 - 2w >= 50?

Feb 9, 2017

$w \le 15$

#### Explanation:

First, subtract $\textcolor{red}{80}$ from each side of the inequality to isolate the $w$ term while keeping the inequality balanced:

$80 - \textcolor{red}{80} - 2 w \ge 50 - \textcolor{red}{80}$

$0 - 2 w \ge - 30$

$- 2 w \ge - 30$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 2}$ to solve for $w$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality condition:

$\frac{- 2 w}{\textcolor{b l u e}{- 2}} \textcolor{red}{\le} \frac{- 30}{\textcolor{b l u e}{- 2}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}} w}{\cancel{\textcolor{b l u e}{- 2}}} \textcolor{red}{\le} 15$

$w \le 15$

##### Impact of this question
302 views around the world
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "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, "math_score": 0.7974993586540222, "perplexity": 411.08447066636967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655908294.32/warc/CC-MAIN-20200710113143-20200710143143-00555.warc.gz"}