SOLUTION: The question is solve the inequality for Algebra II 3x-4/x+3<2 what is the solution? May I have step by step. Thank you so much

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Question 978999: The question is solve the inequality for Algebra II
3x-4/x+3<2 what is the solution? May I have step by step. Thank you so much
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Suspecting that inequality is written incorrectly, maybe the correct inequality being (3x-4)/(x+3)<2,

The solution may go this way:
%283x-4%29%2F%28x%2B3%29%3C2

%283x-4%29%2F%28x%2B3%29-2%3C0

%283x-4%29%2F%28x%2B3%29-2%28%28x%2B3%29%2F%28x%2B3%29%29%3C0

%283x-4-2x-6%29%2F%28x%2B3%29%3C0

%28x-10%29%2F%28x%2B3%29%3C0-----------You want to find how the expression for the left member will be negative...

Do you know how to finish this? Can you identify the critical x values?

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!

1.  Let us assume that the denominator  x+3  is greater than  0:

x + 3 > 0,     i.e.   x > -3.

Then the inequality  %283x-4%29%2F%28x%2B3%29 < 2  is equivalent to the inequality
3x-4 < 2%28x%2B3%29.

(we simply multiplied both sides of the original inequality by the positive multiplier - denominator, and kept the sign of the inequality  "as is").

Solve it step by step:

3x - 4 < 2x + 6,
x < 6 + 4 = 10.

Thus  -3 < x < 10  is the solution of the given inequality.


2.  Next, assume that the denominator  x+3  is lesser than  0:

x + 3 < 0,     i.e.   x < -3.

Then the inequality  %283x-4%29%2F%28x%2B3%29 < 2  is equivalent to the inequality
3x-4 > 2%28x%2B3%29.

(we simply multiplied both sides of the original inequality by the negative multiplier - denominator,  and accordingly changed the sign of the inequality to the opposite one).

Solve it step by step:

3x - 4 > 2x + 6,
x > 6 + 4 = 10.

Thus this alternative lead us to the two two inequalities x < -3 and x > 10.  Obviously, they can not be true simultaneously.  So,  this alternative has no solution.

The only solution is the first alternative solved in n.1.

Answer. The solution of the given inequality is  -3 < x < 10.


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The question is solve the inequality for Algebra II
3x-4/x+3<2 what is the solution? May I have step by step. Thank you so much
%283x+-+4%29%2F%28x+%2B+3%29+%3C+2, with x+%3C%3E+-+3, so one of the critical values is at: -+3

3x - 4 < 2(x + 3) ------- Multiplying by LCD, x + 3

3x - 4 < 2x + 6

3x - 2x < 6 + 4

x < 10



This now gives us the 2 critical values: - 3 and 10, and the 3 intervals: 

1) x < - 3

2) - 3 < x < 10, and

3) x > 10

 

You'll now need to determine which intervals contain values that satisfy the original inequality. Doing this results in the solution: highlight_green%28-+3+%3C+x+%3C+10%29