Final answer:
To solve the inequality -7 < 3x - 4 ≤ 5, you need to isolate x in the middle section of the inequality. Start by adding 4 to all parts of the inequality and then divide all parts of the inequality by 3 to find the solution: -1 < x ≤ 3.
Step-by-step explanation:
To solve the inequality -7 < 3x - 4 ≤ 5, we need to isolate x in the middle section of the inequality.
1. Start by adding 4 to all parts of the inequality: -7 + 4 < 3x - 4 + 4 ≤ 5 + 4, which simplifies to -3 < 3x ≤ 9.
2. Then divide all parts of the inequality by 3: -3/3 < 3x/3 ≤ 9/3, which simplifies to -1 < x ≤ 3.
Therefore, the solution to the inequality is -1 < x ≤ 3.