Question

use the order of operations to evaluate: \\(-7.6 - 29 + (-6.8)\\)
first, simplify the parentheses: \\(9 + (-6.8) = 2.2\\). now the expression is: \\(-7.6 - 2(2.2)\\).
since there are no exponents in this problem, the next step is dropdown
simplify the previous step and you get \\(-7.6 - 4.4\\).
the final answer is \\(-12\\).

dropdown options:
\\((-7.6)2.2\\)
\\((-7.6) - 2\\)
\\((-2)2.2\\)
\\(2.22\\)

Explanation:

Identify the current expression and next operation

The problem asks us to evaluate the expression \(-7.6 - 2[9 + (-6.8)]\) using the order of operations.
The first step simplified the brackets: \([9 + (-6.8)] = 2.2\).
This leaves us with the expression: \(-7.6 - 2(2.2)\).

According to the order of operations (PEMDAS/GEMS), after grouping symbols and exponents, we must perform multiplication and division from left to right before addition and subtraction.
In the expression \(-7.6 - 2(2.2)\), the operations are:

1. Subtraction: subtracting from \(-7.6\)
2. Multiplication: multiplying \(-2\) by \(2.2\) (or multiplying \(2\) by \(2.2\) and then subtracting).

Therefore, the next step is to perform the multiplication.

Match the next step with the options

We need to identify which option represents the multiplication step that yields the next simplified expression.
The multiplication part of the expression is \(2(2.2)\) or including the sign, \((-2)2.2\).
Let's look at the dropdown options shown in the image:

• \((-7.6)2.2\)
• \((-7.6) - 2\)
• \((-2)2.2\)
• \(2.22\)

The option \((-2)2.2\) correctly represents the multiplication operation that needs to be performed next. Multiplying \(-2\) by \(2.2\) results in \(-4.4\), which matches the subsequent step shown in the image: \(-7.6 - 4.4\).

Verify the final calculation

Once the multiplication is performed:

$$ -7.6 - 2(2.2) = -7.6 - 4.4 $$

Now, perform the subtraction:

$$ -7.6 - 4.4 = -12 $$

This matches the final answer of \(-12\) shown in the image, confirming that the correct choice for the dropdown is \((-2)2.2\).

Answer:

• (A) \((-7.6)2.2\)
• (B) \((-7.6) - 2\)
• (C) \((-2)2.2\) (Correct answer)
• (D) \(2.22\)