math/algebra
posted by jan kopelman on .
solve the compound inequality.
2x7 / 6 is less than or equal to 7, or 2x7 / 6 is greater than or equal to 5
I came up with 35/2 or 37/2 but it's incorrect. help?!!

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 >= (2X7) / 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 liketerms:
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.