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.