# How do you solve |x + 3| = (x-2)?

Apr 14, 2017

No solution

#### Explanation:

Since absolute values are always nonnegative,

$| x + 3 | = x - 2 \ge q 0 R i g h t a r r o w x \ge q 2$,

which means that $x + 3$ is nonnegative.

So, the equation becomes (by simply removing the absolute value sign)

$R i g h t a r r o w x + 3 = x - 2$

By subtracting $x$ from both sides,

$R i g h t a r r o w 3 = - 2$,

which is false.

Hence, there is no solution.

I hope that this was clear.

Apr 14, 2017

No real solution.

#### Explanation:

We have

$\left\mid x + 3 \right\mid = x + 3 - 5$ or assuming $x \ne - 3$

$1 = \frac{x + 3}{\left\mid x + 3 \right\mid} - \frac{5}{\left\mid x + 3 \right\mid}$ so there are two possibilities

$\left\{\begin{matrix}1 = 1 - \frac{5}{\left\mid x + 3 \right\mid} \\ 1 = - 1 - \frac{5}{\left\mid x + 3 \right\mid}\end{matrix}\right.$

and in both cases there is not a real solution for the equations.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8523154,"math_prob":1.0000063,"size":549,"snap":"2021-21-2021-25","text_gpt3_token_len":139,"char_repetition_ratio":0.108256884,"word_repetition_ratio":0.0,"special_character_ratio":0.24772313,"punctuation_ratio":0.12149533,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99998116,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-20T20:22:48Z\",\"WARC-Record-ID\":\"<urn:uuid:aef67bd5-b2df-45e9-82d7-1c9810a55615>\",\"Content-Length\":\"34793\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8ed9ea10-295f-4251-9ce0-57d8c980f312>\",\"WARC-Concurrent-To\":\"<urn:uuid:202bfe8a-6491-4f75-bf26-38fc18722060>\",\"WARC-IP-Address\":\"216.239.36.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-solve-x-3-x-2-3\",\"WARC-Payload-Digest\":\"sha1:A4JT75WVBVEXFRDZOPYRIOCLL4HDYG2V\",\"WARC-Block-Digest\":\"sha1:QXXMDCZ5OJI3RPBOBXDZDOR5VDBAHKJ5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488253106.51_warc_CC-MAIN-20210620175043-20210620205043-00390.warc.gz\"}"}