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

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

Mathematics
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plz I really need help
break this up. Do this one first \[2x-3 < x + 2\]

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Other answers:

is it -1x<2x ?
|dw:1441890766597:dw|
then do \(x+2 \le 3x+5\)
start by subtracting 3x from both sides
it would be the same wouldn't it?
usually not.
is it -2+2<5?
after subtracting 3
where did your x go? You should have -2x + 2 < 5 Then subtract the 2 from both sides
oops yeah forgot to put the x
-2x<3?
right then divide by -2 and flip the sign since it's negative
-1x>0.67?
x > -0.67 b/c you only flip once you divide by the negative
also, you should leave it as \(x>-\frac{2}{3}\) because it's more exact
ok
If you were to graph the two solutions it would look like this|dw:1441891511708:dw|
But your final answer combines them|dw:1441891692074:dw|
So the solution is all numbers between -2/3 and 5, including 5 and you'd write it as \[-\frac{ 2 }{ 3 }
ok thanks so much I really appreciate your help
you're welcome

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