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

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)   (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:

-----------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)   (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 < is equivalent to the inequality
< .

(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 < is equivalent to the inequality
> .

(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)   (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

, with , so one of the critical values is at:
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:
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