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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.
I am looking the domain of g^2-6g-55/g. The denominator here can be also be written as 1g, right?
Ask questionteachme how to graph points convert fractions to deciams #Minimum 100 words accepted#
determine slope of 2y = -x + 10
Example If 8 ×10 14 joules of energy is released at the time of an earthquake what was the magnitude of the earthquake? Solution There actually isn't much to do here o
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3x/4 = 2
x=4y=12 i dont know how to do this can you please help me??!!
i need help on my homework could u help me ?
If a firm sellings its product at a price $p per unit, customers would buy q units per day where q = 1,350 - p. The cost of producing q units per day is $C(q) where C(q) = 50q + 36
one no. is 7 more than another and its square is 77 more than the square of the smaller number.What are the numbers?
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