To find the correct expression for \( A \) that makes the equation \( A = 5 - \frac{11}{3} \) true, we first need to simplify \( 5 - \frac{11}{3} \).
We can express \( 5 \) as a fraction with a denominator of \( 3 \): \[ 5 = \frac{15}{3} \] Now subtract \( \frac{11}{3} \): \[ A = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]
Now, we need to identify which of the response options equals \( \frac{4}{3} \).
Let's analyze each option:
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Option 1: \( A = \frac{12}{3} + \frac{1}{3} \) \[ \frac{12}{3} = 4 \quad \text{and} \quad \frac{1}{3} \quad \Rightarrow \quad 4 + \frac{1}{3} = 4 \frac{1}{3} \quad \text{(not } \frac{4}{3}\text{)} \]
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Option 2: \( A = \frac{15}{3} + \frac{1}{3} \) \[ \frac{15}{3} = 5 \quad \text{and} \quad \frac{1}{3} \quad \Rightarrow \quad 5 + \frac{1}{3} = 5 \frac{1}{3} \quad \text{(not } \frac{4}{3}\text{)} \]
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Option 3: \( A = \frac{12}{3} - \frac{1}{3} \) \[ \frac{12}{3} = 4 \quad \text{and} \quad \frac{1}{3} \quad \Rightarrow \quad 4 - \frac{1}{3} = 4 - 0.33 = 3.67 \quad \text{(not } \frac{4}{3}\text{)} \]
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Option 4: \( A = -\frac{12}{3} + \frac{1}{3} \) \[ -\frac{12}{3} = -4 \quad \text{and} \quad \frac{1}{3} \quad \Rightarrow \quad -4 + \frac{1}{3} = -4 + 0.33 = -3.67 \quad \text{(not } \frac{4}{3}\text{)} \]
None of the options simplifies to \( \frac{4}{3} \).
Based on the analysis, none of the expressions provided are correct for \( A = 5 - \frac{11}{3} \).
If these were to be options tied to other transformations, please double-check as there may be a discrepancy in the choices or in the simplification task.