Equivalent Expressions
This is a very important topic in algebra. You will be doing a lot of simpifying before you graduate from high school.
I would like each of you to comment on the following:
Use CAS or a graphing calculator to determine whether the expressions are equivalent.
abs(x + 10) - 2 and x + 8
Be sure to reset your calculator to default settings. Your comment should be in paragraph form although you may use mathematical symbols like I did. Please check your spelling and grammar.
8 comments:
The expressions are not equivalent. This is because the absolute value of x+10 will always be positive. For x+8, the sum could be negative. For example, if x=-13, then abs(-13+10)-2 would be 1. For -13+8,the answer would be 5.
To determine if there is equivalence, I used my graphing calculator. Even though it looks as though they are equal at first, they aren't. With "standard window settings," they appear to be the same, but if you go to table, when x=-#, the outcomes differ. You have to change your window settings to view the differences on the graphs.
The expressions are not equivalent. At first they look the same when you view the expressions in a standard window however,when you look at the table they are not equivalent when x equals a negative number. For example when x equals -33 then abs(33+10)- 2 = 21 and -33+8 = - 25. -25 does not equal 21. Therefore, abs(x+10) - 2 is not equivalent to x+8.
wuwhogal and gofigure. Are you sure you were accurate when you talked about negative values of x? Please review your responses.
The expressions are not equivalent because abs(x+10)-2 can only be negative when x equals -11, -10, and -9. abs(-11+10)-2 and abs(-9+10)-2 both equal -1 and abs(-10+10)-2 is -2. x+8 can be negative as long as x is a negative number less than -8. For example -20+8 is -12 but -7+8 is 1.
Tommy, check your first statement again. Are you talking about negative values for the expression (range)or negative values for the domain of the variable? Can either expression equal a negative number?
No, the expressions abs(x+10)-2 and x+8 are not equivalent. By looking at a graph in standard window settings, you would not be able to tell any difference, but if you looked at a table, you would see they are not equivalent. The expression does work for some numbers, but x does not work for any number less than or equal to -11.
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