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
Mr. Rodriquez comments on a recent test. "well, the class average on the test is exactly 83. if I take away the best score, the average is exactly 82." if there are 16 students in

Vertical asymptote In our graph as the value of x approaches x = 0 the graph begin gets extremely large on both sides of the line given by x = 0. This line is called a vertical


solve each equation for given variable 3ab-2bc=12;

Translate into an equation: A number increased by 19 equals 77 (let the number be represented by k)

how do I change 0.68 to a fraction or mixed number

REENA HAS PENS AND PENCILS WHICH TOGETHER ARE 40 IN NUMBER.IF SHE HAS 5 MORE PENCILS AND 5 LESS PENS,THEN THE NUMBER PENCILS WOULD BECOME 4 TIMES THE NUMBER OF PENS.FIND THE ORIGIN

can you help me solve this problem?


1. Find out all the zeroes of the polynomial and their multiplicity.  Utilizes the fact above to find out the x-intercept which corresponds to each zero will cross the x-axis or on