The answer is (-infinity, -(11/7)) or [(-239/166), inifinty). I just need to know how to work the problem.
2007-07-04 13:08:55 · 6 answers · asked by Tiffany W 2 in Science & Mathematics ➔ Mathematics
Multiply by 7x+11, but you have to be aware that multiplying by a negative number flips the inequality.
(a) 7x+11 > 0 (inquality NOT flipped):
(14-5x)/ (7x+11) >= 23
14 - 5x >= 23 (7x + 11)
14 - 5x >= 253 + 161x
166x <= -239
x <= -239/166
Note, though that 7x+11 > 0 implies that x > -11/7, so this solution is
-11/7 < x <= -239/166
(x is between approximately -1.57 and -1.44)
(b) 7x+11 < 0 (inequality IS flipped):
(14-5x)/ (7x+11) >= 23
14 - 5x <= 23 (7x + 11)
14 - 5x <= 253 + 161x
166x >= -239
x >= -239/166
Note, though that 7x+11 < 0 implies that x < -11/7, and all numbers less than -11/7 are NOT greater than -239/166, so there are no solutions for this case.
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I don't see how you get to +/- infinity with your suggested answer. As x approaches positive or negative infinity, the equation's result approaches -5/7, which is not greater or equal to 23.
The answer that I get is only a very small range
-11/7 < x <= -239/166, which makes 7x+11 a small number in the denominator, which makes the answer large.
Perhaps your question was "LESS THAN or equal to 23"? In that case, the answer is all numbers not covered in that small range, and excluding -11/7 (which places a zero in the denominator).
2007-07-04 13:14:14 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
(14-5x) / (7x+11) ≥ 23
(14-5x) / (7x+11) -23 ≥ 0
[14-5x-23*(7x+11)]/(7x+11) ≥ 0
-[ 166x+239]/(7x+11) ≥ 0
Therefore,
If 166x+239 ≥ 0 , then (7x+11) < 0 , which leads to
x ≥ -239/166 and x < -11/7
No solution
If 166x+239 ≤ 0 , then (7x+11) > 0 , which leads to
x ≤ -239/166 and x ≥-11/7
Solution: -11/7 < x ≤ -239/166
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The answer (-infinity, -(11/7)) or [(-239/166), infinity) is obviously not right. If x is a very large positive number, then the LHS is negative.
2007-07-04 13:24:40 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋
(14-5x)/ (7x+11) >= 23
14-5x >= 23(7x+11)
14-5x >= 161x + 253
-166x >= 239
x <= -239/166
Note that there is a discontinuity when x = -11/7 (division by 0)
Thus (14-5x)(7x+11) is always negative when x<-11/7.
The inequality only holds for -11/ 7
The answers given above are incorrect.
2007-07-04 19:12:34 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
you % to start by ability of removing the variable interior the denominator by ability of multiplying the two components by ability of 7x+11. this leaves you with: 14-5x is decrease than or equivalent to 23 (7x+11). do the multiplication on the nicely suited facet and you get: 14-5x is decrease than or equivalent to 161x+253. upload 5x to the two components. now you have 14 is decrease than or equivalent to 166x +253. subtract 253 from the nicely suited hand facet. now you have -239 is decrease than or equivalent to 166x. divide the two components by ability of 166. -239/166 is decrease than or equivalent to x. wish this facilitates !
2016-10-19 02:16:06 · answer #4 · answered by ? 4 · 0⤊ 0⤋
x is less than or equal to 1.439
2007-07-04 16:58:51 · answer #5 · answered by anwarideen i 1 · 0⤊ 0⤋
greater than
2007-07-04 13:13:39 · answer #6 · answered by Anonymous · 0⤊ 1⤋