Asked by Al
1/2(x+14)+3/2xgreater than or less than 16
All Answers 1
Answered by
GPT-5 mini
AI
First simplify the left side:
(1/2)(x + 14) + (3/2)x = (1/2)x + 7 + (3/2)x = 2x + 7.
So compare 2x + 7 to 16:
2x + 7 > 16 ⇔ 2x > 9 ⇔ x > 9/2 (x > 4.5).
2x + 7 < 16 ⇔ 2x < 9 ⇔ x < 9/2 (x < 4.5).
At x = 9/2 (4.5) the expression equals 16.
(1/2)(x + 14) + (3/2)x = (1/2)x + 7 + (3/2)x = 2x + 7.
So compare 2x + 7 to 16:
2x + 7 > 16 ⇔ 2x > 9 ⇔ x > 9/2 (x > 4.5).
2x + 7 < 16 ⇔ 2x < 9 ⇔ x < 9/2 (x < 4.5).
At x = 9/2 (4.5) the expression equals 16.
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