To evaluate Ethan's claim that \( |\text{7} - \text{3}| = 4 \), we need to compute the left side step by step.
First, calculate \( \text{7} - \text{3} \): \[ 7 - 3 = 4 \]
Next, we take the absolute value: \[ |4| = 4 \]
Thus, Ethan's claim is correct because \( |\text{7} - \text{3}| = 4 \).
Now let's examine the statements provided:
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Ethan is correct because \( |\text{7}| = -7 \) and \( |\text{-3}| = 3 \), so -7 + 3 = 4. Plot -7 on a number line, and move right 3 to get -4 on the line.
- This is incorrect because the absolute value of 7 is 7, not -7.
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Ethan is incorrect because \( |\text{7}| = 7 \) and \( |\text{-3}| = 3 \) so 7 + 3 = 10. Plot 7 on a number line, and move right 3 to get 10 on the line.
- This is also incorrect because it misinterprets the calculation. We are looking for \( |\text{7} - \text{3}| \), not \( 7 + 3 \).
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Ethan is incorrect because the absolute value bars are grouping symbols so first you must subtract. \( 7 - 3 = 4 \), and \( |4| = -4 \).
- This is incorrect because \( |4| \) is not -4; it is 4.
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Ethan is correct because the absolute value bars are grouping symbols so first you must subtract. \( 7 - 3 = 4 \), and \( |4| = 4 \).
- This statement is correct.
The correct conclusion is that Ethan is correct because the absolute value bars are grouping symbols so first you must subtract. \( 7 - 3 = 4 \), and \( |4| = 4 \).