Solve the compound inequality. Express your answer using inequality signs, and then write your answer in interval notation. 5y<7-2y<9+y

Answer 1

When you have a compound inequality with the variable in all three parts, it is probably easier to see what is happening if you break it apart into two inequalities joined by the word "AND".

5y < 7 - 2y AND 7 - 2y < 9 + y

Now solve each separately:

7y < 7 AND -2 < 3y

y < 1 AND -2/3 < y

Rewrite so smallest part is on the left:

-2/3 < y < 1

Check 0:

5(0) < 7 - 2(0) < 9 + (0)

0 < 7 < 9

Check -1/2:

5(-1/2) < 7 - 2(-1/2) < 9 + (-1/2)

-5/2 < 8 < 8 1/2

Check 1/2:

5(1/2) < 7 - 2(1/2) < 9 + (1/2)

5/2 < 6 < 9 1/2

Interval notation:

(-2/3 , 1), that is, the solution is all numbers between -2/3 and 1.

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