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

Rduce the equation to quadratic form, Solve following equations.        ...

Solve following equations.                                         y -6 - 9 y -3 + 8 = 0 Solution y -6 - 9 y -3 + 8 = 0 For this part notice that, -6 = 2 (

Number and expressions, Ask ques1. Isaac goes to an amusement park where ti...

Ask ques1. Isaac goes to an amusement park where tickets for the rides cost $10 per sheet and tickets for the shows cost $15 each. (a) Write an expression that describes the amount

Graphing cubic functions, how to graph f(x)=-x to the 3rd minus 3 using tra...

how to graph f(x)=-x to the 3rd minus 3 using transformations

Domain and range, Consider the function y = 2x. the domain is restricted to...

Consider the function y = 2x. the domain is restricted to 0 = x = 4, what is the range of this function

Example of absolute value inequalities, Solve following.  2 x - 4 = 10 ...

Solve following.  2 x - 4 = 10 Solution There actually isn't much to do other than plug into the formula.  As with equations p merely represents whatever is within the a

I just don''t get it, Determine which system below will produce infinitely ...

Determine which system below will produce infinitely many solutions. 2x + 5y = 24 2x + 5y = 42 3x - 2y = 15 6x + 5y = 11 4x - 3y = 9 -8x + 6y = -18 5x - 3y = 16 -2x + 3y =

I need help, Do you accept screen shot because it is a graph.

Do you accept screen shot because it is a graph.

Equations, solve the system of equations using the substitution method. y+5...

solve the system of equations using the substitution method. y+5x=10 -10x+3y=5

Measure of central tendency.., the set of data shows of score of 25 student...

the set of data shows of score of 25 students in their periodical test. 34 35 40 40 48 21 20 19 34 45 19 17 18 15 16 21 20 18 17 10 19 17 29 45 50 1. what score is typical t

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