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Solve the following inequality algebraically. ∣x−5∣ + 11 <= 18

 Apr 13, 2022

Best Answer 

 #1
avatar+578 
+3

\(\left|x-5\right|+11\le \:18\)

\(\left|x-5\right|+11-11\le \:18-11\)

\(\left|x-5\right|\le \:7\)

 

\(\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a\)

 

\(-7\le \:x-5\le \:7\)

 

\(x\ge \:-2\quad \mathrm{and}\quad \:x\le \:12\)

 

\(== -2\le \:x\le \:12\)

 

smiley

.
 Apr 13, 2022
 #1
avatar+578 
+3
Best Answer

\(\left|x-5\right|+11\le \:18\)

\(\left|x-5\right|+11-11\le \:18-11\)

\(\left|x-5\right|\le \:7\)

 

\(\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a\)

 

\(-7\le \:x-5\le \:7\)

 

\(x\ge \:-2\quad \mathrm{and}\quad \:x\le \:12\)

 

\(== -2\le \:x\le \:12\)

 

smiley

Vinculum Apr 13, 2022
 #2
avatar+124594 
0

Very nice, Vinculum  !!!!!

 

 

cool cool cool

CPhill  Apr 13, 2022

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