Final answer:
The expression -3/4(5p-12)+2(8-1/4p) simplifies to -17/4p + 25 by distributing the constants, combining like terms, and eliminating terms where possible.
Step-by-step explanation:
To simplify the expression -3/4(5p-12)+2(8-1/4p), we will distribute the constants within the brackets:
Multiply -3/4 by 5p and -12 to get -15/4p + 9.
Multiply 2 by 8 and -1/4p to get 16 - 1/2p.
Now combine like terms:
-15/4p + 9 + 16 - 1/2p = (-15/4p - 1/2p) + (9 + 16)
To combine the p terms, we need a common denominator:
-15/4p - 2/4p = -17/4p
Add the constants:
9 + 16 = 25
So the expression simplifies to:
-17/4p + 25
Always remember to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.