SOLUTION: This problem does not come from a book but from a worksheet so here it is: Solve the rational inequality. Type -INFINITY if you need or INFINITY if you need. 5/x+1 is greate

Algebra ->  Algebra  -> Inequalities -> SOLUTION: This problem does not come from a book but from a worksheet so here it is: Solve the rational inequality. Type -INFINITY if you need or INFINITY if you need. 5/x+1 is greate      Log On

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Question 104875: This problem does not come from a book but from a worksheet so here it is:
Solve the rational inequality. Type -INFINITY if you need or INFINITY if you need.
5/x+1 is greater than or equal to 1/x
I would appreciate your reply by tomorrow. THANKS!
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the inequality:
1) 5%2F%28x%2B1%29+%3E=+1%2Fx or is it?
2) 5%2Fx+%2B+1+%3E=+1%2Fx
1) 5%2F%28x%2B1%29+%3E+=1%2Fx Multiply both sides by (x+1)
1) 5%3E=%28x%2B1%29%2Fx Now multiply both sides by x.
5x%3E=+x%2B1 Subtract x from both sides.
4x+%3E=+1 Finally divide both sides by 4.
x+%3E=+1%2F4 This is the answer for 1) but, if it's 2)
2) 5%2Fx+%2B+1%3E=+1%2Fx Multiply both sides by x.
5x%2Fx+%2B+x+%3E=+1 Simplify.
5%2Bx+%3E=1 Subtract 5 from both sides.
x+%3E=+-4 This is the answer for 2)
Hint: Use parentheses to clarify the intent of the problem.
In your problem you could have written:
(5/x)+1 or 5/(x+1) to remove any ambiguity.