Question

Simplify the expression.
-3/4(5p-12) + 2(8-1/4p)

Answer 1

The given algebraic expression has been simplified by distributing coefficients into each set of parentheses, combining like terms, and simplifying to get the result -13/4p - 7.

Step-by-step explanation:

To simplify the algebraic expression -3/4(5p - 12) + 2(8 - 1/4p), we will follow several algebraic steps, which include distribution, combining like terms, and simplification:

1. Distribute -3/4 across the terms inside the first parentheses: -3/4 * 5p + 3/4 * 12.
2. Distribute 2 across the terms inside the second parentheses: 2 * 8 - 2 * 1/4p.
3. Combine the distributed terms to get: -15/4p + 9 - 16 + 1/2p.
4. Combine like terms p and constant terms to simplify the expression further, which gives us: -13/4p - 7.
5. Check if the answer is reasonable by ensuring that all like terms have been combined and the expression is fully simplified.

In the end, the simplified expression is -13/4p - 7.