My name is Julien Maes and I have always been very interested in math and it has been one of , if not my favorite subject. I like math because I am able to learn new concepts and how to solve different problems. In math 25 we are exposed to H.O.T problems , which are Higher order thinking problems. These problems really get you thinking about the different equations to use and many other things. On this page I will be showing you Inequalities, what they are and how they function.
This is a picture of and inequality being graphed on a line. As you can see when the inequality is showing the a number is less than or equal to 11 the bubble is closed because it is on that number or less. And when a number is just simply larger than 11 it is an open bubble because it is any number lager than 11.
20.5
This is an image of problem 20.5. This problem said that two people are solving an inequality and they both solve it the same way but when it comes to the final step one of them forgets to flip the sign when it is divided by the negative. The question was how any hours past noon will the water be 36 inches + above the flood gate
This is showing that every hours past 24 hours, including the 24th hour, the water level will be at least 36 inches above the flood gate. This is the correct equation to use because the question in the problem set before was asking , how many hours after noon will the water be 36, or more, above the flood gate.
20.6
This is the follow up question to 20.5 . After hearing Alex’s suggestion about using a test value to check an in- equality, Cameron suggests that the problem could have been done by solving the equation 132 − 4x = 36 first. Complete the reasoning behind this strategy.
Instead of using inequalities we used an equal sign (=) to find what X was actual equal to.
Instead of using inequalities we used an equal sign (=) to find what X was actual equal to.
20.7
Deniz, who has been keeping quiet during the discussion, remarks, “The only really tricky thing about inequalities is when you try to multiply them or divide them by negative numbers, but this kind of step can be avoided altogether. Cameron just told us one way to avoid it, and there is another way, too.” Explain this remark by Deniz.
Well Deniz is saying that if you were to add 4x first to both sides instead of subtracting 132 first you will be able to keep the entire equation positive instead of the equation being negative because of the -4x.
See no messing with negatives , WOW!
Well Deniz is saying that if you were to add 4x first to both sides instead of subtracting 132 first you will be able to keep the entire equation positive instead of the equation being negative because of the -4x.
See no messing with negatives , WOW!
22.8
Can you think of a number k for which k2 < k is true? Graph all such numbers on a number line. Also describe them using words, and using algebraic notation.
For example the number I used was 0.5.
For example the number I used was 0.5.
Here is the line graph representing the numbers that are eligible to be represented by the variable K.
30.4
It is common practice to read −75 < 2 as “−75 is less than 2.” Yet, in a significant sense, it is really −75 that is the larger of the two numbers! Discuss the two meanings of “less than.”
In this problem it is completely true that -75 is less than 2 in the sense that -75 is a negative number and 2 is positive. On the other hand 75 is larger number than 2 but it is still negative on the number line.
One meaning of less than is when one number is smaller than the other. And the other is, even if a number is larger then the other but the larger number is negative and the smaller number is positive, the smaller number will actually be higher on a number line because it is positive.
In this problem it is completely true that -75 is less than 2 in the sense that -75 is a negative number and 2 is positive. On the other hand 75 is larger number than 2 but it is still negative on the number line.
One meaning of less than is when one number is smaller than the other. And the other is, even if a number is larger then the other but the larger number is negative and the smaller number is positive, the smaller number will actually be higher on a number line because it is positive.
23.10
Find all the values of x that make 0.1x + 0.25(102 − x) < 17.10 true.
First, for this problem I went back to problem 23.8 which had asked us to solve for X in the equation 0.1x + 0.25(102 − x) = 17.10and I got the answer of X=56 so I plugged in a few numbers , larger and smaller , like 55 and 57 and I came to the conclusion that when the number of the variable is larger than the equation will be true but when the number is less than 56 the equation is not true.
First, for this problem I went back to problem 23.8 which had asked us to solve for X in the equation 0.1x + 0.25(102 − x) = 17.10and I got the answer of X=56 so I plugged in a few numbers , larger and smaller , like 55 and 57 and I came to the conclusion that when the number of the variable is larger than the equation will be true but when the number is less than 56 the equation is not true.