1
Question
Solve the inequality 6 ≤ –3(2x – 4) < 12
Solve the inequality 6 ≤ –3(2x – 4) < 12
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Solution
6 ≤
– 3(2x
– 4) < 12
⇒ 2
≤
–(2x
– 4) < 4
⇒ –2
≥
2x –
4 > –4
⇒ 4
– 2 ≥
2x > 4
– 4
⇒ 2
≥
2x > 0
⇒1
≥
x > 0
Thus,
the solution set for the given inequalityis (0, 1].
6 ≤ – 3(2x – 4) < 12
⇒ 2 ≤ –(2x – 4) < 4
⇒ –2 ≥ 2x – 4 > –4
⇒ 4 – 2 ≥ 2x > 4 – 4
⇒ 2 ≥ 2x > 0
⇒1 ≥ x > 0
Thus, the solution set for the given inequalityis (0, 1].
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