Solving the inequalities, Algebra

Inequalities Involving > and ≥

Once again let's begin along a simple number example.

                                                    p ≥ 4

It says that whatever p is it has to be at least a distance of 4 from the origin and thus p has to be in one of the following two ranges,

                                 p ≤ -4                         or                                        p ≥ 4

Before giving the general solution we have to address a common mistake which students make with these types of problems.  Several students try to join these into a single double inequality as follows,

                                                          -4 ≥ p ≥ 4

Whereas this might appear to make sense we can't stress sufficient that THIS IS NOT CORRECT!! Remind what a double inequality says.  In a double inequality we need that both of the inequalities be satisfied simultaneously. Then the double inequality above would mean that p is a number which is simultaneously smaller than -4 and larger than 4. It just doesn't make sense. There is no number which satisfies this.

These solutions have to be written as two inequalities. Here is the general formula for these.

If         p          ≥ b, b = 0         then     p ≤ -b   or  p ≥ b

If         p          > b, b = 0         then     p < -b   or  p > b

Posted Date: 4/6/2013 5:41:52 AM | Location : United States







Related Discussions:- Solving the inequalities, Assignment Help, Ask Question on Solving the inequalities, Get Answer, Expert's Help, Solving the inequalities Discussions

Write discussion on Solving the inequalities
Your posts are moderated
Related Questions


1.(x+y+1)² 2.(x+y-1)² 3.(x-y-1)² 4.(-x-y-1)² question: what is the effect of switching the plus sign to minus sign on the product


A mountain has an elevation of 19,389 feet in 1918, the glacier on this peak covered 4 acres. By 2003 this glacier had melted to 1 acre. What was the yearlyrate of change and what


what is the perpendicular line for y= -x= -3;(-2,-2)

approximate pi to the nearest one thousandths1

Now, let's get back to parabolas. There is a basic procedure we can always use to get a pretty good sketch of a parabola. Following it is.  1. Determine the vertex. We'll discus

Solve following.                                  |2x - 5 |= 9 Solution Now, recall that absolute value does not just make all minus signs in plus signs. In order to sol