True inequality, Algebra

Assignment Help:

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.


Related Discussions:- True inequality

parametric equations, A motile cell is placed at the point (x0, y0) on a s...

A motile cell is placed at the point (x0, y0) on a square shaped dish filled with a "nutrient bath". The concentration of nutrient at any point (x, y) in the dish is given by N(

Angles and sides, what is the missing angle of 37 degree and 92 drgees

what is the missing angle of 37 degree and 92 drgees

Angles of triangle, The measure of the smallest angle is one-third the larg...

The measure of the smallest angle is one-third the largest angle. The measure of the middle angle is 65 less than the measure of the largest angle. Find the measures of the angles

Process for graphing a polynomial, 1. Find out all the zeroes of the polyno...

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

Find out the partial fraction, Example: Find out the partial fraction deco...

Example: Find out the partial fraction decomposition of following.              8x - 42 / x 2 + 3x -18 Solution The primary thing to do is factor out the denominator as

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd