When it comes to answering questions about inequalities, it is important to remember the signs and what they represent. In this instance, we need to find a range of solutions where 2(3x+1) is greater than 3-4x.

To solve this inequality, we need to make x the subject of the inequality. First, we need to expand 2(3x+1) to get 6x+2. Now we have the inequality 6x+2>3-4x. Next we rearrange to make x the subject. By adding 4x to both sides and subtracting 2 from both sides, we get the inequality 10x>1. Finally, we divide both sides by 10 to get x by itself. The simplified inequality is x>1/10. Therefore the answer to the question is the range of solutions for the inequality 2(3x+1)>3-4x is x is greater than 1/10.

((2x + 3)/(x-4)) - ((2x-8)/(2x+1)) = 1

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