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For which values of x is ?
Indicate all possible values of x.
Title
Rational Expression Inequality
Your Result
Correct
Difficulty
Medium
Your Pace
0:03
Others' Pace
2:09
Video Explanation
Text Explanation
Do a little algebra first. Add 1/5 to both sides
Scanning the list, we see that we are only concerned with positive numbers. If all the numbers involved are positive, we can cross multiply, so do that.
Again, because we know that we are concerned only with positive values of x, we can divide by x.
13 < x
This makes it very clear. Notice that x can't equal 13, because this is a strict inequality. It must be all the values greater than 13: {14, 15, 16}.
Answers = (E), (F), & (G)
FAQ: I thought multiplying or dividing by a variable in an inequality was bad? Why exactly are we allowed to do that here?
For inequalities, if we multiply/divide by a positive number then the inequality sign remains the same. However, if we multiply/divide by a negative number then the inequality sign flips. Now, the tricky part about variables is that we have no idea whether the variable is a negative number or a positive number, so we have no idea whether we should flip or keep the inequality sign if we multiply/divide by the variable. Because we don't know what to do, we CAN'T multiply/divide by a variable.
However, in this case, by seeing that all the answer choices are positive, we know that the variable must have a positive value! So keep in mind that you may find useful information about how to solve a problem by glancing at all the available answer choices. Again, since all the answer choices are positive, that means that x must represent a positive value. Thus, we can go ahead and multiply/divide by the variable!
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