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4-2x >= 1-x Which of the following best describes the solutions to the inequality shown? Choose 1 answer: (A) x <= 1 (B) x >= 3 (C) x <= 3 (D) x <= -5

4−2x≥1−x 4-2 x \geq 1-x \newlineWhich of the following best describes the solutions to the inequality shown?\newlineChoose 11 answer:\newline(A) x≤1 x \leq 1 \newline(B) x≥3 x \geq 3 \newline(C) x≤3 x \leq 3 \newline(D) x≤−5 x \leq-5

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Full solution

Q. 4−2x≥1−x 4-2 x \geq 1-x \newlineWhich of the following best describes the solutions to the inequality shown?\newlineChoose 11 answer:\newline(A) x≤1 x \leq 1 \newline(B) x≥3 x \geq 3 \newline(C) x≤3 x \leq 3 \newline(D) x≤−5 x \leq-5
  1. Add xx to both sides: Simplify the inequality by adding xx to both sides: 4−2x+x≥1−x+x4 - 2x + x \geq 1 - x + x
  2. Subtract 44 from both sides: This simplifies to 4−x≥14 - x \geq 1; now subtract 44 from both sides: 4−4−x≥1−44 - 4 - x \geq 1 - 4
  3. Multiply by −1-1 and flip: This results in −x≥−3-x \geq -3; multiply both sides by −1-1 (and remember to flip the inequality sign): −1(−x)≤−1(−3)-1(-x) \leq -1(-3)
  4. Final result: Simplified, this gives x≤3x \leq 3

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