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The 8 problems from the 01 HW: Solving Inequalities & Interval Notation worksheet — solve each, note the graph, and give interval notation — with full step-by-step solutions.
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Medium Solve, then write the solution in interval notation: \(-3x - 7x \le -8x - 6\).
Answer: A — \(x \ge 3\); interval \([3,\,\infty)\)
Medium Solve, then write in interval notation: \(13 - 2n < 1 - 4n\).
Answer: D — \(n < -6\); interval \((-\infty,\,-6)\)
Medium Solve, then write in interval notation: \(-2(-8r - 2) < -92\).
Answer: A — \(r < -6\); interval \((-\infty,\,-6)\)
Medium Solve, then write in interval notation: \(6(1 + 7n) + 5 < -325\).
Answer: C — \(n < -8\); interval \((-\infty,\,-8)\)
Medium Solve, then write in interval notation: \(165 < 5(-5x + 8)\).
Answer: C — \(x < -5\); interval \((-\infty,\,-5)\)
Medium Solve, then write in interval notation: \(-8(k - 7) \ge 120\).
Answer: D — \(k \le -8\); interval \((-\infty,\,-8\,]\)
Hard Solve, then write in interval notation: \(1 - 6(1 - 2x) \le 3(4x + 1) - 8\).
Answer: A — all real numbers; interval \((-\infty,\,\infty)\)
Hard Solve, then write in interval notation: \(7v - 3(-6 - v) > -8(-v - 1)\).
Answer: A — \(v > -5\); interval \((-5,\,\infty)\)