# How do you solve and write the following in interval notation: x − 3>8 AND x + 2 >?

Jan 13, 2018

Question is missing a value; see below for an approach using a variable in place of the missing value.

#### Explanation:

Suppose the intended restrictions were
$\left.\left(x - 3 > 8 , \text{ AND } , x + 2 > \textcolor{b l u e}{n}\right)\right.$

Since you can add or subtract the same amount to both sides of an inequality without changing the validity or direction of the inequality,
these are equivalent to
$\left.\left(x > 11 , \text{ AND } , x > \left(\textcolor{b l u e}{n} - 2\right)\right)\right.$

Using the notation: $\max \left(a , b\right) = \left\{\begin{matrix}a \text{ if " a>=b \\ b" if } a < b\end{matrix}\right.$

Then these restrictions can be combined into the single restriction:
$x > \max \left(8 , \textcolor{b l u e}{n} - 2\right)$
or
in the requested interval notation:
$x \in \left(\max \left(8 , \textcolor{b l u e}{n} - 2\right) , + \infty\right)$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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, "url": "https://socratic.org/questions/how-do-you-solve-and-write-the-following-in-interval-notation-x-3-8-and-x-2", "fetch_time": 1560937653000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2019-26/segments/1560627998943.53/warc/CC-MAIN-20190619083757-20190619105757-00498.warc.gz", "warc_record_offset": 591556009, "warc_record_length": 6074, "token_count": 307, "char_count": 978, "score": 4.25, "int_score": 4, "crawl": "CC-MAIN-2019-26", "snapshot_type": "latest", "language": "en", "language_score": 0.7068508863449097, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00061-of-00064.parquet"}