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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.
(^5square root of 38)^3 Round your answer to 2 decimal places A.8.9 B.8.86 C.8.87 D.429.51
r+7= r=3
.what is the average rate of change if f(x) = 4x + 6 .
Example : Sketch the graph of hyperbolas. ( x - 3) 2 /25 - ( y + 1) 2 /49 =1 Solution Now, notice that the y term contain the minus sig
(b+a)+[-(a+0+b)]=0
Assume that P ( x ) is a polynomial along with degree n. Thus we know that the polynomial have to look like, P ( x ) =ax n
How do you expand a sigma notation from x to x of a variable that is not defined in the index. For example, summation of i=1 to n of x?
Find a three-digit positive integers such that the sum of all three digit is 14, the tens digit is two more than ones and if the digit is reversed, the number is unchanged.
find the average rate of change of the function f(x)=4x from X1=0 to x2=6
Use (fog)(4), (gof)(4), (fog)(x), and (gof)(x) 1.) f(x)=x^2+1 and g(x)=x+5
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