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Solve the compound inequality. Give the solution set in both interval and graph forms. -4x <= -8" or "-4x >= 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is ◻ (Type your answer in interval notation.) B. The solution set is O/.

Solve the compound inequality. Give the solution set in both interval and graph forms.\newline−4x≤−8 or −4x≥0 -4 x \leq-8 \text { or }-4 x \geq 0 \newlineSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.\newlineA. The solution set is □ \square \newline(Type your answer in interval notation.)\newlineB. The solution set is ∅ \varnothing .

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Q. Solve the compound inequality. Give the solution set in both interval and graph forms.\newline−4x≤−8 or −4x≥0 -4 x \leq-8 \text { or }-4 x \geq 0 \newlineSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.\newlineA. The solution set is □ \square \newline(Type your answer in interval notation.)\newlineB. The solution set is ∅ \varnothing .
  1. Divide and Flip Inequality: Divide both sides of the first inequality by −4-4, remembering to flip the inequality sign because we're dividing by a negative number: −4x≤−8-4x \leq -8 becomes x≥2x \geq 2.
  2. Solve Second Inequality: For the second inequality, −4x≥0-4x \geq 0, divide both sides by −4-4, again flipping the inequality sign, to get x≤0x \leq 0.
  3. Combine Solutions: Now we have two inequalities: x≥2x \geq 2 and x≤0x \leq 0. Since it's an ＂or＂ compound inequality, we combine the solutions.
  4. Interval Notation: The solution set in interval notation is (−∞,0](-\infty, 0] ∪\cup [2,∞)[2, \infty).
  5. Graph Solution: To graph the solution, shade the region to the left of 00 including 00 and the region to the right of 22 including 22.

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