Absolute value equations and inequalities

9000027304

Level: 
A
Identify the solution set of the following inequality. \[ |x - 1| > 10 \]
\(\left (-\infty ;-9\right )\cup \left (11;\infty \right )\)
\(\left (-\infty ;9\right )\cup \left (11;\infty \right )\)
\(\left [ 11;\infty \right )\)
\(\left (-\infty ;10\right )\cup \left [ 11;\infty \right )\)

9000027306

Level: 
A
Identify the solution set of the following inequality. \[ |x + 3|\geq 6 \]
\(\left (-\infty ;-9\right ] \cup \left [ 3;\infty \right )\)
\(\left (-\infty ;3\right ] \cup \left [ 6;\infty \right )\)
\(\left (-\infty ;-3\right )\cup \left (9;\infty \right )\)
\(\left [ -3;6\right ] \)

9000026403

Level: 
B
To solve the equation with absolute value using interval method we have to divide the domain of the equation by the zero points of the subexpressions in the absolute value. Find all these points. \[ |x + 1| + |2x - 1| = 3 \]
\(-1,\ \frac{1} {2}\)
\(- 3\)
\(1,\ -\frac{1} {2}\)
\(0\)

9000026404

Level: 
B
To solve the equation with absolute value using interval method we have to divide the domain of the equation by the zero points of the subexpressions in the absolute value. Find all these points. \[ 2|x - 2| + |2 - x| = 1 + |x| \]
\(2,\ 0\)
\(-2,\ 2,\ 0\)
\(-1,\ 2\)
\(-1,\ 2,\ 0\)