Final answer:
The expression equivalent to (5 + 9)(1 – 2) – 9.1 – 6 is -29.1, obtained by simplifying inside the parentheses, multiplying, and then subtracting in accordance with the order of operations and addition/subtraction rules.
Step-by-step explanation:
To find an expression equivalent to the given expression (5 + 9)(1 – 2) – 9.1 – 6, we need to follow the proper order of operations, which is parentheses first, then multiplication, and finally addition and subtraction. We'll also apply the rules of adding and subtracting positive and negative numbers as we proceed.
Step 1: Simplify inside the parentheses (5 + 9) and (1 – 2). 5 + 9 = 14
1 – 2 = -1
Step 2: Multiply the results from the parentheses.
14 × -1 = -14
Step 3: Subtract the products of the multiplication from the remaining terms.
-14 – 9.1 – 6 = -14 - 9 - 1 - 0.1 - 6 = -29.1
When we eliminate terms wherever possible and apply the rules of operation, we find that the expression equivalent to the original is -29.1.
It's always important to check the answer to see if it is reasonable. In this case, the arithmetic has been done carefully to ensure each step conforms to the expected mathematical operations and the properties of real numbers.