Ethan claims that StartAbsoluteValue 7 minus 3 EndAbsoluteValue = 4. Which statement about Ethan’s claim is true?

Ethan is correct because StartAbsoluteValue 7 EndAbsoluteValue = negative 7 and StartAbsoluteValue negative 3 EndAbsoluteValue = 3 so –7 + 3 = 4. Plot –7 on a number line, and move right 3 to get –4 on the line.
Ethan is incorrect because StartAbsoluteValue 7 EndAbsoluteValue = 7 and StartAbsoluteValue negative 3 EndAbsoluteValue = 3 so 7 + 3 = 10. Plot 7 on a number line, and move right 3 to get 10 on the line.
Ethan is incorrect because the absolute value bars are grouping symbols so first you must subtract. 7 minus 3 = 4, and StartAbsoluteValue 4 EndAbsoluteValue = negative 4.
Ethan is correct because the absolute value bars are grouping symbols so first you must subtract. 7 minus 3 = 4, and StartAbsoluteValue 4 EndAbsoluteValue = 4.

1 answer

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:

  1. 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.
  2. 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 \( 7 + 3 \).
  3. 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.
  4. 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 \( |4| = 4 \).