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
a car wash at the local gas station costs $10.95 including tax. How many car washes can you get at the gas station and still pay less than Plan A: 3 Coupons Coupon Booklet $32.99 P

Now it is time to look at solving some more hard inequalities.  In this section we will be solving (single) inequalities which involve polynomials of degree at least two.  Or, to p

how do you do equations for sloe intercept?


x^2 + 7x + 12 factor fully

Tickets for the school play cost $6 for students and $9 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2610. How many student and how

Name the property illustrated by the following? x + (-x)=0


The "humps" where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points .  If we know that the polynomial con