Jeffrey Z. answered • 12/11/14
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You're close, Steve, with the next steps!
It appears that you've chosen to distribute the multiplication in parentheses in each side of the inequality and then collect like terms, and that's not a bad idea. The -30x, -32x, and -140 are all correct. I am getting -84 instead of -57 on the left-hand-side, however. The inequality becomes:
-30x - 84 > -32x - 140
I bring the "x" 's to the left and constants to the right and get:
2x > -56 or x > -28.
In interval notation this would be: (-28,+∞)
A crude character line graph:
------------------------------O======================================>
-28 0
Jeff
Steve N.
Actually one more thing how did you get -84 on the left? You have 9(-3x-12)-3(x-8) Would it not be -27x-81 and -3x +24 ?
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12/11/14
Jeffrey Z.
Let's just look at the left-hand side: 9(-3x-12)-3(x-8)
Put the "9" and the "3" with what they are multiplying: (-(9*3)x-(9*12))-((3*1)x-(3*8))
(The "1" in the 3rd term is the assumed coefficient of x)
Do all 4 multiplications: (-27x-108)-(3x-24)
Getting rid of the parentheses: -27x - 108 - 3x + 24
Combining like terms gives the "-30x - 84" I initially showed.
The "-84" is the sum of "-108" and "+24". You were missing the -108=9*-12. This product is NOT -81!
Jeff
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12/11/14
Steve N.
Nevermind I see my error, thank you very much for the help
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12/11/14
Steve N.
12/11/14