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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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How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality. Consider responding to a classmate by determining whether or not the solution ...
Weegy: Substitute the value for the variable and do whatever arithmetic is necessary to see if you have a true statement or not. If the statement is true, the value is an element of the solution set. [ If the statement is false, it is not an element of the solution set. How is this different from determining if a value is a solution to an equation? The method is not different. If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Answer: Yes, but only if the inequality sign is the "or equal" variety. For example, given the equation x=5, replace the equal sign with a 'greater than or equal' sign: x%3E=5. In this case, 5 is an element of the solution set for both the equation and the inequality. However, given the same equation and replacing the equal sign with a 'greater than' sign results in this inequality: x%3E5. In this case, the equation and the inequality have no elements of their solution sets in common. There is only one element in the solution set to the equation, namely the number 5. There are an infinite number of elements in the solution set to the inequality, but none of those elements are the number 5. ] (More)
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Asked 6/28/2011 6:51:41 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: A person uses those control structures to make all decisions in which they encounter. Repetition is an unconscious form in which the mind makes based on re-occurring. [ Selection is an automatic choice a person makes based on the ideals they have learned in the past. There are many factors and structures which will change ideals and the best methods are to stay structured from previous teachings. ] (More)
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Asked 6/28/2011 7:59:29 PM
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