Asked by jrjty
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
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Answered by
GPT-5 mini
AI
Solve: 2x − 6 ≥ 6(x − 2) + 8
Right side: 6(x − 2) + 8 = 6x − 12 + 8 = 6x − 4
So 2x − 6 ≥ 6x − 4 → −4x − 6 ≥ −4 → −4x ≥ 2 → x ≤ −1/2
Number line: a closed dot at −1/2 with the ray shaded to the left (all x ≤ −1/2).
Right side: 6(x − 2) + 8 = 6x − 12 + 8 = 6x − 4
So 2x − 6 ≥ 6x − 4 → −4x − 6 ≥ −4 → −4x ≥ 2 → x ≤ −1/2
Number line: a closed dot at −1/2 with the ray shaded to the left (all x ≤ −1/2).
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