True inequality, Algebra

We have to give one last note on interval notation before moving on to solving inequalities. Always recall that while we are writing down an interval notation for inequality that the number onto the left has to be the smaller of the two.

Now it's time to begin thinking about solving linear inequalities. We will employ the following set of facts in our solving of inequalities.  Note down that the facts are given for <. However we can write down an equivalent set of facts for the remaining three inequalities.

1.   If a < b  then a + c < b + c and a - c < b - c for any number c.  In other term, we can add or subtract a number to both of sides of the inequality & we don't vary the inequality itself.

2.   If a < b and c > 0 then ac

3.   If a < b and c<0 then ac > bc  and a/c >   b/c .  In this case, unlike the earlier fact, if c is negative we have to flip the direction of the inequality while we multiply or divide both sides by the inequality through c.

These are closely the similar facts that we utilized to solve linear equations. The single real exception is the third fact. It is the important issue as it is frequently the most misused and/or forgotten fact in solving inequalities.

If you aren't certain that you believe that the sign of c matters for the second & third fact assume the following number instance.

                                                                   -3 < 5

This is a true inequality.  Now multiply both of sides by 2 and by -2.

- 3 < 5                                                                         - 3 < 5

-3( 2) < 5 ( 2)                                                             -3 ( -2) < 5 ( -2)

- 6 < 10                                                                         6 < -10

Sure enough, while multiplying by a +ve number the direction of the inequality remains the similar, however while multiplying by a -ve number the direction of the inequality does change.

Posted Date: 4/6/2013 5:23:15 AM | Location : United States







Related Discussions:- True inequality, Assignment Help, Ask Question on True inequality, Get Answer, Expert's Help, True inequality Discussions

Write discussion on True inequality
Your posts are moderated
Related Questions
Ask question #15/16 to the percentage

A kilometer is about 5/8 mile.About how many miles are in 4 2/5 kilometers? How would I set a proportion?


Completing the Square The first method we'll learning at in this section is completing the square. This is called it since it uses a procedure called completing the square in t

Example : determine the zeroes of following polynomials. P ( x)= 5x 5 - 20x 4 +5x3 + 50x2 - 20x - 40 = 5 (x + 1) 2 ( x - 2) 3 Solution In this the factoring has been


The integral arises in probability theory. (a) Consult the library or Internet to find how this integral relates to the calculationof a probability using the Normal dist

Bills Roast Beef sells 3 times as many sandwiches as Pete''s deli. The difference between their sales is 170 sandwiches. How many sandwiches did each sell?


my son is in middle school and his teacher pre-algebra teacher wants him to write a summary on "who I am " about his self. summary about myself. I need your to know do have a any