Question

Please help.

Answer 1

The answer is B) x < 17 25/153.

The first thing we do to solve this equation is rewrite all of the fractions using a common denominator.  The LCD for 2, 4 and 3 is 12:

(12 9/12)x + 24 6/12 < 243 4/12

Subtract 24 6/12 from both sides:
(12 9/12)x + 24 6/12 - 24 6/12 < 243 4/12 - 24 6/12
(12 9/12)x < 218 10/12 (we lack 2/12 from being able to subtract, so we borrow)

Divide both sides by 12 9/12:
(12 9/12)x ÷ (12 9/12) < (218 10/12) ÷ (12 9/12)

Convert both mixed numbers to improper fractions:
x < (2626/12) ÷ (153/12)

Multiply by the reciprocal:
x < (2626/12) × (12/153)
x < 2626/153
x < 17 25/153