Expressions and equations
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Please provide an answer to the questions below that contains 250 to 300 words to each.
1.If a < b, then -a > -b, Why? Illustrate your reasoning with several examples.
2.How can you differentiate between an equation and an expression? Give several examples of each.
3.How does the knowledge of simplifying an expression help you to solve an equation efficiently? Give an example of using and not using simplification to illustrate your reasoning.
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Solution Summary
This provides explanations of three discussion questions, involving an equality, the difference between an equation and an expression, and simplifying expressions.
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1. If a < b, then -a > -b, Why? Illustrate your reasoning with several examples.
This relationship comes from the rules of multiplication in inequalities. The inequality is preserved if both sides are multiplied or divided by a positive number. The inequality is reversed if both sides are multiplied or divided by a negative number. If both sides are multiplied by 0, the inequality changes into an equality. Take for example the relationship 8 > 4. If we multiply both sides by 3, a positive number, we get 24 > 12, which we know is true. However, if we multiply both sides by -3, a negative number, it is noticeable that -3*8 = -24 which is in fact less than -3*4 = -12. Therefore, we should state -24 < -12, i.e., the inequality has been reversed. This observation is also true if one or both the sides are negative, or are fractions. For example, if -5 < -2, and if we multiply both the sides by -1, then (-5)*(-1) should be greater than (-2)*(-1) , or 5 should be greater than 2, which it indeed is. Similarly, if (2/7) > (1/3), then -4*(2/7) should be less than (-4)*(1/3), or -8/7 < -4/3, which is again true. IT is also noticeable that no ...
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