Final answer:
To solve the compound inequality -1 <= (5x+1)/4 < 5, we solved two separate inequalities yielding the solution -0.8 <= x < 3.8.
Step-by-step explanation:
To solve the compound inequality -1 ≤ (5x+1)/4 < 5, we need to solve for x in two separate inequalities and then find the intersection of both solutions. For the first inequality, we multiply by 4 on both sides to get -4 ≤ 5x+1. Subtracting 1 from both sides yields -5 ≤ 5x, which simplifies to x ≤ -0.8. For the second inequality, after multiplying both sides by 4, we obtain 5x+1 < 20. Subtracting 1 from both sides gives us 5x < 19, which simplifies to x < 3.8. Therefore, the solution to the compound inequality is -0.8 ≤ x < 3.8.