Final answer:
To solve the inequality {2x+3}/{5x-1} ≥ 2, we can start by multiplying both sides of the inequality by the denominator {5x-1} to eliminate it from the left side. Then, solve the resulting linear inequality algebraically and find the solution on a number line.
Step-by-step explanation:
To solve the inequality {2x+3}/{5x-1} ≥ 2, we can start by multiplying both sides of the inequality by the denominator {5x-1} to eliminate it from the left side. This gives us {2x+3} ≥ 2({5x-1}). Next, distribute the 2 on the right side to get 2x+3 ≥ 10x-2. Now, we can solve this inequality by moving all the x terms to one side and all the constants to the other side. Subtracting 2x and adding 2 to both sides, we get 5 ≥ 8x.
Dividing both sides by 8, we find that x ≤ 5/8. Therefore, on a number line, the solution to the inequality {2x+3}/{5x-1} ≥ 2 is x ≤ 5/8.