Final answer:
To solve the inequality (x+1)/(2x-3)>2, multiply both sides by 2x-3 to eliminate the fraction, simplify, and solve for x. The solution is x<7/3.
Step-by-step explanation:
To solve the inequality (x+1)/(2x-3)>2, follow these steps:
- Start by multiplying both sides of the inequality by 2x-3 to eliminate the fraction: (2x-3)(x+1)/(2x-3)>2(2x-3)
- This simplifies to x+1>2(2x-3)
- Distribute 2 to both terms inside the parentheses: x+1>4x-6
- Next, subtract x from both sides to isolate the variable: 1>3x-6
- Add 6 to both sides: 7>3x
- Finally, divide both sides by 3 to solve for x: x<7/3
Therefore, the solution to the inequality is x<7/3.