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agasfer [191]
3 years ago
14

Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5. Show your work.

Mathematics
2 answers:
mixas84 [53]3 years ago
6 0

Answer:

-3/2 ≤ x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x + 5

2x - 3 < x + 2  

2x - x -3 < x - x + 2

x - 3 < 2  

x - 3 + 3 < 2 + 3

x < 5  

x + 2 ≤ 3x + 5  

x - x + 2 ≤ 3x - x + 5

2 ≤ 2x + 5  

2 - 5 ≤ 2x + 5 - 5

-3 ≤ 2x  

(1/2) -3 ≤ 2x (1/2)

-3/2 ≤ x  

-3/2 ≤ x < 5

Paul [167]3 years ago
4 0
2x − 3 < x + 2 
<span>x − 3 < 2 </span>
<span>x < 5 </span>

<span>x + 2 ≤ 3x + 5 </span>
<span> 2 ≤ 2x + 5 </span>
<span> -3 ≤ 2x </span>
<span> -3/2 ≤ x </span>

<span>Answer: -3/2 ≤ x < 5</span>
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