Meehan98
  • Meehan98
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Mathematics
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
AlexandervonHumboldt2
  • AlexandervonHumboldt2
yeah
AlexandervonHumboldt2
  • AlexandervonHumboldt2
i'm here
Meehan98
  • Meehan98
\[\left| 2x1 \right|\le 11\]

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AlexandervonHumboldt2
  • AlexandervonHumboldt2
what does 1 after x means?
Meehan98
  • Meehan98
I got: \[x \le 5 or x \ge 5\]
Meehan98
  • Meehan98
Sorry..(2x+1)
AlexandervonHumboldt2
  • AlexandervonHumboldt2
oh
mathstudent55
  • mathstudent55
When solving an absolute inequality of this type, you need to change the absolute value inequality into a compound inequality (without absolute value signs.)
Meehan98
  • Meehan98
So, 2x+1=11 which would make x=5
mathstudent55
  • mathstudent55
\(|X|\le k\) Here, X stands for an expression in x, and k is a non-negative number. Solve this compound inequality: \(-k \le X \le k\)
mathstudent55
  • mathstudent55
N ow we look at your absolute value inequality. \(|2x + 1| \le 11\) It becomes: \(-11 \le 2x + 1 \le 11\) Now we solve the compound inequality. Subtract 1 from all 3 sides: \(-12 \le 2x \le 10\) Divide all 3 sides by 2: \(-6 \le x \le 5\) Which means the same as \(x \ge -6\) and \(x \le 5\)
Meehan98
  • Meehan98
Oh, thank you! That helps so much!
mathstudent55
  • mathstudent55
You're welcome. If the absolute value inequality has a \(\gt\) or a \(\ge\), then this is what you do: \(|X| \gt k\) becomes \(X \lt -k\) or \(X \gt k\) In this case, the compound inequality has the word "or" instead of "and".

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