Final answer:
The equivalent expression for -12(-4/1+8)-7(-5/4+4) simplifies to -75.25, after distributing the multipliers and combining like terms according to the rules of algebra.
Step-by-step explanation:
To combine like terms and find the equivalent expression for -12(-4/1+8)-7(-5/4+4), we follow the standard rules of algebra for adding, subtracting, multiplying, and dividing numbers.
Firstly, distribute the -12 across the terms within the parentheses:
- -12 * (-4/1) = 48
- -12 * 8 = -96
Then, distribute the -7 across the terms within the following parentheses:
- -7 * (-5/4) = 35/4 or 8.75
- -7 * 4 = -28
Add the results of these distributions together:
- 48 + (-96) + 8.75 + (-28) = -75.25
Therefore, the equivalent expression simplifies to -75.25.
Important Concepts in Algebra:
When two negative numbers multiply, the answer is positive.
When a negative and a positive number multiply, the answer is negative.
- Adding two numbers with opposite signs involves subtracting the smaller number from the larger one, and the result takes the sign of the larger number.