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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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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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I really liked all of your examples for sequential, repetition, and selection. I especially liked your example for selection about the money. That is a selection that we all make almost everyday. There are so many different ways and options to pay with cash depending on what is in your pocket. Sometimes you have to make a selection based on what you currently have, all while keeping in mind that you may need cash and certain bills for future purchases. what do you think about this?
Weegy: Financial goals provide a sense of direction to your cash budget. Common financial goals include saving up cash to provide for a first-time home purchase, college education or retirement lifestyle. [ You will categorize each financial goal according to time frame and total costs. For example, you may need to amass $2 million to provide for an Oregon coast retirement within the next 20 years. Savings Projections You will make savings projections with the help of an online financial calculator. The financial calculator helps you to toggle through different figures for savings amounts and rates of return that will help you to arrive at a future lump sum of cash. After using the financial calculator, you can estimate the amount of money you need to be saving each month to meet your goals. With this information, you will analyze your current finances to determine whether your goals are actually realistic. To do so, you will subtract your current monthly expenses away from income and calculate free cash flow available to save towards your goals. If your goals appear out of reach, you may need to put in more time at work and also cut expenses to increase cash flow. To manage a cash budget, you must separate discretionary spending from committed expenses. Discretionary spending goes towards the purchase of consumer items that are not necessary for survival and do not add value to your bottom line. Consumer goods and services may therefore include concert tickets, designer clothes and fine restaurant dining. You will eliminate discretionary spending from your budget altogether if you are having trouble paying bills and achieving your financial goals. In certain situations, a discretionary purchase can motivate you to get your finances in order. Perhaps you will treat yourself to a Caribbean cruise, after paying off all credit card debt and saving $15,000 in cash reserves. Committed Expenses Committed expenses are necessary to observe the law, ... (More)
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Asked 7/1/2011 11:14:27 AM
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