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Notes
Problems
Solve for x.
\(\textbf{1)}\) \( |x|=3 \)
\(\textbf{2)}\) \( |x|=5 \)
\(\textbf{3)}\) \( |x-2|=5 \)
\(\textbf{4)}\) \( |x+1|=4 \)
\(\textbf{5)}\) \( |x+1|=-2 \)
\(\textbf{6)}\) \( |2x+5|=11 \)
\(\textbf{7)}\) \( |4x+2|=10 \)
\(\textbf{8)}\) \( 2|x-2|+4=12 \)
\(\textbf{9)}\) \( 2|x+6|-2=16 \)
\(\textbf{10)}\) \( |x-2|=-5 \)
\(\textbf{11)}\) \( |x-4|=0 \)
\(\textbf{12)}\) \( |x+2|=-8 \)
\(\textbf{13)}\) \( |2x+1|=15 \)
\(\textbf{14)}\) \( |2x-1|=9 \)
Challenge Problem
\(\textbf{15)}\) \( |x|=-x\)
\(\textbf{16)}\) \( |3x-|x||=16\)
True or False
\(\textbf{17)}\) The statement \(|a−b|=|b−a|\) is always true for any real numbers \(a\) and \(b\).\(\)
\(\textbf{18)}\) If \(|a| \lt |b|\), then \(a \lt b\)
\(\textbf{19)}\) If \(|c|=-2\), then \(c\) must be either \(2\) or \(-2\).
\(\textbf{20)}\) If \(|a−b|=0\), then \(a=b\).
\(\textbf{21)}\) If \(n\gt |m|\), then \(n\) is positive.
See Related Pages\(\)
\(\bullet\text{ Absolute Value Equation Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Absoluate Value Inequalities}\)
\(\,\,\,\,\,\,\,\,|5-2x|\le10…\)
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Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
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