Answer:
To show that the expression 3b - 4 + 6(b - 9) is equivalent to the expression 9(b - 6) - 4, you can simplify each expression and demonstrate that they yield the same result. Here's the step-by-step work:
Expression 1: 3b - 4 + 6(b - 9)
1. Distribute 6 to the terms inside the parentheses:
3b - 4 + 6b - 54
2. Combine like terms:
(3b + 6b) - 4 - 54
9b - 4 - 54
3. Further simplify by subtracting 4 and 54 from 9b:
9b - 58
Expression 2: 9(b - 6) - 4
1. Distribute 9 to the terms inside the parentheses:
9b - 54 - 4
2. Combine like terms:
(9b - 4) - 54
Now, compare the two simplified expressions:
Expression 1: 9b - 58
Expression 2: (9b - 4) - 54
Expression 1 and Expression 2 are indeed equivalent because they both simplify to 9b - 58.
So, the expressions are equal, demonstrating their equivalence.
Explanation: