Question
Simplify the expression. If the expression cannot be simplified, so state. \[ 9 x-[5 x-(2 x-3 y)]-8 y \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The result is B. The expression cannot be simplified.
Ask by Hardy Todd. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result is \(6x - 11y\).
Solution
**A. The result is**
\[ 6x - 11y \]
**Simplification Steps:**
1. Start with the original expression:
\[ 9x - [5x - (2x - 3y)] - 8y \]
2. Simplify the innermost parentheses:
\[ 5x - (2x - 3y) = 5x - 2x + 3y = 3x + 3y \]
3. Substitute back into the original expression:
\[ 9x - (3x + 3y) - 8y = 9x - 3x - 3y - 8y \]
4. Combine like terms:
\[ (9x - 3x) + (-3y - 8y) = 6x - 11y \]
Thus, the simplified expression is \(6x - 11y\).
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Simplify this solution Beyond the Answer
To simplify the expression \( 9x - [5x - (2x - 3y)] - 8y \), we start by simplifying inside the brackets: First, simplify \( 2x - 3y \): \[ - (2x - 3y) = -2x + 3y \] Now substitute this back into the expression: \[ 9x - [5x - 2x + 3y] - 8y \] Now simplify \( 5x - 2x + 3y \): \[ 5x - 2x = 3x \] So, we have: \[ 9x - [3x + 3y] - 8y \] Next, simplify: \[ - [3x + 3y] = -3x - 3y \] Substituting it all back gives: \[ 9x - 3x - 3y - 8y \] Combine like terms: \[ (9x - 3x) + (-3y - 8y) = 6x - 11y \] So the final simplified expression is: \[ 6x - 11y \] A. The result is \( 6x - 11y \)
