SOLUTION: Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5, Can you show your work if possible, thanks!
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Question 860174: Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5, Can you show your work if possible, thanks!
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
This is one of my favorites and the solution is straight forward and something you need to remember.
Given:
(1) 2x - 3 < x + 2 <= 3x + 5
You solve this using the "left-side inequality" then the "right-side inequality". That is we write (1) as TWO inequalities;
(2) 2x - 3 < x + 2 and
(3) x + 2 <= 3x + 5
Now solve for x in (2).
(4) 2x - x < 2 + 3 or
(5) x < 5
Now solve for x in (3).
(6) 2 - 5 <= 3x - x or
(7) -3 <= 2x or
(8) -3/ <= x
Now recombine (5) and (7), keeping the order least to most left-to-right
(9) -3/2 <= x < 5
Answer: the solution to the inequality is -3/2 <= x < 5.
Thanks for reading
Now remember, solve two simple inequalities instead of staring at it and saying "What'll I do?"
PS You can also do this for longer strings of inequalities!
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