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Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to
solve. In your inequality, use both the multiplication and addition properties of inequalities. Consider solving your classmates’ inequalities. Explain how you arrived at your answers. Also, help other students who may be having difficulty solving inequalities. Ask clarifying questions if you need additional assistance.
An inequality states that one number is less than (or greater than) another. [ I think the best way to understand what happens when you multiply or divide an inequality by a negative number is to picture the situation, before and after, on the number line Picture any two numbers on the number line. The one on the left is less than the one on the right. (The one on the right is greater than the
one on the left.) This is true whether the two numbers are both positive, both negative, a negative and a positive or zero and any number. When you multiply (or divide) any non-zero number by a negative, its sign changes. If it was positive it becomes negative and if it was negative it becomes positive. On a number line, the number "flips" over to the other side of zero. When you multiply (or divide) both sides of an inequality this happens to both numbers, the one on the "less than" side and the one on the "greater than" side. Both sides "flip". And when this happens the number that was on the left of the other before is now to the right of the other. In other words, what was less than before is now greater than. (And the number that was to the right (i.e. greater than) ends up to the left of (or less than) the other number.) This is why we have to reverse ("flip") the inequality whenever we multiply or divide it by a negative number. If you're still having trouble with this, try the following: Pick any two (different) numbers. Write the two numbers on the same line with some space between them. Pick any negative number Multiply or divide (your choice) both of the first two numbers by this negative number and write the answers on another line with some space between them. Now, on each line, decide which inequality symbol belongs between the two numbers and write it there. (if you have trouble with this, plot the numbers on a number line. ]
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Asked 6/27/2011 5:55:02 PM
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How do you use the three basic control structures—sequential, repetition, and selection—in your everyday problem solving? Do you think there are any other control structures that would make your problem-solving skills more efficient? If so, describe them
Weegy: Sequential - Choosing what to order for lunch. Same steps every time: 1) Look at the menu, 2) Pick an item, 3) Order the item. Repetition - Finding a parking spot. [ Repeatedly drive around the block until a spot opens up. Selection - Deciding how to pay for something from the change in your pocket. Look at the change you have, and choose the correct coins necessary to pay for your purchase. ] (More)
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Asked 6/27/2011 5:45:25 PM
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The multiplication principle for inequalities that is similar to that for equations. If you multiply on both sides of a negative number, the direction of the inequality symbol must be changed, 4 6x3 what do you think about this?
Weegy: Inequalities The usual total order relation = : N × N can be defined as follows, assuming 0 is a natural number: For all a, b ? N, [ a = b if and only if there exists some c ? N such that a + c = b. This relation is stable under addition and multiplication: for a, b, c \in N , if a = b, then: a + c = b + c, and a · c = b · c. ] (More)
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Asked 6/27/2011 6:03:00 PM
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Why does the inequality sign change when both sides are multiplied or divided by a negative number? This inequality changes because you have changed the values of the inequality, then flip the inequality sign. Once the values become a negative that means that negatives are flipped also. They flip from one side to the other, if both sides were negative. If the sign is not flipped, it makes the solution a whole different range of numbers, because it changes the inequality. Does this happen with ...
Weegy: This form of the induction axiom is a simple consequence of the standard formulation, but is often better suited for reasoning about the = order. [ For example, to show that the naturals are well-ordered—every nonempty subset of N has a least element—one can reason as follows. Let a nonempty X ? N be given and assume X has no least element. Because 0 is the least element of N, it must be that 0 ? X. For any n ? N, suppose for every k = n, k ? X. Then S(n) ? X, for otherwise it would be the least element of X. Thus, by the strong induction principle, for every n ? N, n ? X. Thus, X n N = Ø, which contradicts X being a nonempty subset of N. Thus X has a least element. ] (More)
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Asked 6/27/2011 6:07:33 PM
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Then, think about the pseudocode algorithm you would write for a simple task, such as making a peanut butter sandwich, for example, as well as three simple control structures that could be used to create this algorithm. What do you think is the most difficult part of creating the algorithm? What can you do to make this process easier?
Weegy: The most difficult part of creating the algorithm would be converting an everyday activity to mathematical terms. I really can't think of a way to make it easier, it has to be done if you want to create the algorithm. (More)
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Asked 6/28/2011 6:28:20 PM
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How do you use the three basic control structures—sequential, repetition, and selection—in your everyday problem solving? Do you think there are any other control structures that would make your problem-solving skills more efficient? If so, describe them.
Weegy: "When I need to solve a problem, I generally start by writing down as many ideas as I can think of about possible causes. Next I look for relationships among causes so I can group together symptoms of bigger problems. [ Usually, after I study these groups of problems, the real cause becomes readily apparent ] (More)
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Asked 6/28/2011 6:39:54 PM
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