SOLUTION: Solve the inequality 2x - 3 < x + 2 &#8804; 3x + 5 You dont need to graph it I just need help solving it, thanks

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Question 851772: Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5
You dont need to graph it I just need help solving it, thanks
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
2x - 3 < x + 2 ≤ 3x + 5

1. Separate these into two different inequalities:

2x - 3 < x + 2 AND x + 2 ≤ 3x + 5

2. Solve for x in each inequality:

2x - 3 < x + 2 -----> x < 5

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

We now know that x must be less than 5 and greater than -3/2. So,

-3/2 ≤ x < 5 which is your final answer.