3 years ago

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
x − 3 < 2 
x < 5 

x + 2 ≤ 3x + 5 
 2 ≤ 2x + 5 
 -3 ≤ 2x 
 -3/2 ≤ x 

Answer: -3/2 ≤ x < 5

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