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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.
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.
what is the area of a polygon.
I have such a hard time understanding them
can you explain to me how to solve x^3+x+5
7w+2=3w+94
Taylor is 7 years younger than Lisa Lila is 3 x Lisa''s age if Lisa''s age is represented by x create an expression that represents the total age of all three girls
#question. in january sunanda changed 25000 pounds into dollars when the exchange rate was $1.96= 1 pounin june she changed the dallars back into when the exchange rate was $1.75=1
Use synthetic division to divide 5x 3 - x 2 + 6 by x - 4 . Solution Okay along with synthetic division we pretty much avoid all the x's and just work with the numbers in
A blue whale gains 2.3 tons a month for the first year of life. If a blue whale weighed 15 tons at birth, how much will it weigh on its first birthday?
What is the solution of 6w-8>22
The weight of an object on Planet A and the weight of the same object on the Planet B are proportional. An astronaut who weighs 160 pounds on Planet A weighs 26.7 pounds on Planet
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