This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the inequality, we need to isolate x. Step 1: Add 2 to all parts of the inequality. -(1)/(2) < -3x - 2 ≤ (1)/(2) -(1)/(2) + 2 < -3x - 2 + 2 ≤ (1)/(2) + 2 -(1)/(2) + (4)/(2) < -3x ≤ (1)/(2) + (4)/(2) (3)/(2) < -3x ≤ (5)/(2) Step 2: Divide all parts by -3. Remember to reverse the inequality signs when dividing by a negative number. (3)/(2)-3 > x ≥ (5)/(2)-3 -(3)/(6) > x ≥ -(5)/(6) -(1)/(2) > x ≥ -(5)/(6) Step 3: Rewrite the inequality with the smaller value on the left. -(5)/(6) ≤ x < -(1)/(2) Step 4: Express the solution in interval notation. The interval is [-(5)/(6), -(1)/(2)). Comparing this with the given options, option D matches our result. The final answer is D. Send me the next one 📸