Questions: -9+[(5-4)-(-7+6)] -9+[(5-4)-(-7+6)]= (Simplify your answer.)

Transcript text: \[ -9+[(5-4)-(-7+6)] \] \[ -9+[(5-4)-(-7+6)]=\square \text { (Simplify your answer.) } \]

Solution

Solution Steps

To simplify the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, simplify the expressions inside the innermost parentheses, then proceed outward.

Step 1: Simplify the Innermost Parentheses

First, we simplify the expression inside the innermost parentheses: \[ -7 + 6 = -1 \] Now, the expression becomes: \[ -9 + [(5 - 4) - (-1)] \]

Step 2: Simplify the Next Parentheses

Next, we simplify \(5 - 4\): \[ 5 - 4 = 1 \] Now, substituting this back into the expression gives us: \[ -9 + [1 - (-1)] \]

Step 3: Final Simplification

Now, we simplify \(1 - (-1)\): \[ 1 - (-1) = 1 + 1 = 2 \] Thus, the expression simplifies to: \[ -9 + 2 = -7 \]