SOLUTION: A couple of questions from my textbook that I need help with. I'm having trouble with rational inequalities.
Solve the following inequalities and give your answer in interval n
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-> SOLUTION: A couple of questions from my textbook that I need help with. I'm having trouble with rational inequalities.
Solve the following inequalities and give your answer in interval n
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Question 949423: A couple of questions from my textbook that I need help with. I'm having trouble with rational inequalities.
Solve the following inequalities and give your answer in interval notation.
a. -3≤ 3-5x/3 <3/8
b. 3x-5/x >0
Hint: Either both the numerator and the denominator are positive, or both are negative; consider both cases.
Thanks.
a. -3≤ 3-5x/3 <3/8
b. 3x-5/x >0
When typing algebra, you must put parentheses around
numerators and denominators if they contain more than
1 letter or 1 number, like this
a. -3≤ (3-5x)/3 <3/8
b. (3x-5)/x >0
----------------------------
Multiply thru all 3 sides by 24
Add -24 to all 3 sides:
Divide through by -40 which reverses
the inequalities
-------------------------------
b. (3x-5)/x >0
Critical values are when numerator equas zero and when
denominator equals zero.
Numerator=0
3x-5 = 0
3x = 5
x = = <-- critical value
Denominator = 0
x = 0
Put critical values on number line:
------------o------o---------------
0
Test any value less than 0, say -1, by substituting
in the original:
That's true so we shade line left of 0
<===========o------o---------------
0
---------------
Next test any value between 0 and , say 1, by substituting
in the original:
That's false so we do not shade line between 0 and . We
still have
<===========o------o---------------
0
-----------------
Test any value right of , say 2, by substituting
in the original:
That's true so we shade line right of
S
<===========o------o==========>
0
Interval notation
Edwin