Solve the equations and inequalities below. Check your solutions, if possible.
Note the absolute value. When is an absolute value greater than or equal to
all real numbers
Factor, and solve for
. Since this is an inequality, these are the boundary points.
The boundary points are
Plot your boundary points on a number line. Test a point in each region to see which region(s) make the inequality true.
This is a quadratic equation. Set it equal to
. Then factor and use the Zero Product Property or use the Quadratic Formula to solve.
Fractions represent division. Multiply all terms by
to 'undo' the denominators.