Answer:
x = 3/4
Step-by-step explanation:
Find the LCD of the fractions. Multiplying the denominators 3 and 4 together, we get LCD = 12.
Rewriting the mixed numbers, we get
3 2/3 = 3 8/12 and 3 1/4 = 3 3/12
So the original equation becomes
(3 8/12)x + 3 3/12 = 6
We must now combine like terms: subtract 3 3/12 from both sides of this equation, obtaining:
(3 8/12)x = 6 - 3 3/12, or
(3 8/12)x = 2 9/12. Converting the mixed numbers into improper fractions, we get:
(44/12)x = 33/12. Multiplying both sides by 12 yields 44x = 33
and so x = 33/44 = 3/4
x = 3/4
Alternatively, convert the original mixed numbers into improper fractions right away. Then the original 3 2/3 x+3 1/4=6
becomes (11/3)x + 13/4 = 72/12, or
(44/12)x + 39/12 = 72/12
Multiplying all three terms by 12 yields:
44x + 39 = 72, which simplifies to 44x = 33, or x = 3/4
