solve the compound inequality.

Question

2x-7 / 6 is less than or equal to -7, or 2x-7 / 6 is greater than or equal to 5

I came up with -35/2 or 37/2 but it's incorrect. help?!!

Answer 1

Jan, your answers has no meaning
without the inequality signs.

I solved this problem with the
assumption that (2X - 7) is the numerator and 6 is the denominator.
If not , then our answers will be wrong.

GIVEN: -7 >= (2X-7) / 6 >= 5.
Multiply by 6:
-42 >= 2X -7 >= 30.
Add 7 to center and both sides:
-42 + 7 >= 2X -7 +7 >= 30 + 7.
Combine terms:
-35 >= 2X >= 37.
Divide center and both sides by 2:
-35 / 2 >= X >= 37 / 2.
You have the correct numbers, but
you'll have to show inequality signs.

A 2nd interpretation:
GIVEN: -7 >= 2X -7/6 >= 5.
Add 7/6 to center and both sides:
-7 + 7/6 >= 2X -7/6 +7/6 >= 5 + 7/6.
-42/7 + 7/6 >= 2X >= 30/6 + 7/6
Combine like-terms:
-35/6 >= 2X >= 37/6.
Multiply center and both sides by 6:
-35 >= 12X >= 37.
Divide both sides and center by 12:
-35/12 >= X >= 37/12.