Answer :
Let's evaluate each equation step-by-step to determine if it is true or false.
Equation A: [tex]\(-7 - 5 + 3 = 1\)[/tex]
1. Start with [tex]\(-7 - 5\)[/tex]:
[tex]\[-7 - 5 = -12\][/tex]
2. Now, add 3:
[tex]\[-12 + 3 = -9\][/tex]
3. Therefore, [tex]\(-7 - 5 + 3 = -9\)[/tex], not 1.
So, equation A is False.
Equation B: [tex]\(-(9 + 11) + 1 = -1\)[/tex]
1. First, evaluate the expression inside the parentheses:
[tex]\[9 + 11 = 20\][/tex]
2. Now, apply the negative sign:
[tex]\[-(20) = -20\][/tex]
3. Add 1:
[tex]\[-20 + 1 = -19\][/tex]
4. Therefore, [tex]\(-(9 + 11) + 1 = -19\)[/tex], not -1.
So, equation B is False.
Equation C: [tex]\(24 - (-6) - 6 = 24\)[/tex]
1. Start with the subtraction of a negative number (which is equivalent to adding):
[tex]\[24 - (-6) = 24 + 6 = 30\][/tex]
2. Now, subtract 6:
[tex]\[30 - 6 = 24\][/tex]
3. Therefore, [tex]\(24 - (-6) - 6 = 24\)[/tex].
So, equation C is True.
Equation D: [tex]\(12 + (-8) - 1 = 3\)[/tex]
1. Add -8 to 12:
[tex]\[12 + (-8) = 4\][/tex]
2. Then, subtract 1:
[tex]\[4 - 1 = 3\][/tex]
3. Therefore, [tex]\(12 + (-8) - 1 = 3\)[/tex].
So, equation D is True.
Equation E: [tex]\(-|2 - 7| + 5 = 0\)[/tex]
1. First, calculate the absolute value:
[tex]\[2 - 7 = -5\][/tex]
[tex]\[|-5| = 5\][/tex]
2. Apply the negative sign:
[tex]\[-|2 - 7| = -5\][/tex]
3. Add 5:
[tex]\[-5 + 5 = 0\][/tex]
4. Therefore, [tex]\(-|2 - 7| + 5 = 0\)[/tex].
So, equation E is True.
Based on the evaluations:
- Equation A: False
- Equation B: False
- Equation C: True
- Equation D: True
- Equation E: True
Here’s the final categorization:
A [tex]\(\square\)[/tex] False
B [tex]\(\square\)[/tex] False
C [tex]\(\square\)[/tex] True
D [tex]\(\square\)[/tex] True
E [tex]\(\square\)[/tex] True
Equation A: [tex]\(-7 - 5 + 3 = 1\)[/tex]
1. Start with [tex]\(-7 - 5\)[/tex]:
[tex]\[-7 - 5 = -12\][/tex]
2. Now, add 3:
[tex]\[-12 + 3 = -9\][/tex]
3. Therefore, [tex]\(-7 - 5 + 3 = -9\)[/tex], not 1.
So, equation A is False.
Equation B: [tex]\(-(9 + 11) + 1 = -1\)[/tex]
1. First, evaluate the expression inside the parentheses:
[tex]\[9 + 11 = 20\][/tex]
2. Now, apply the negative sign:
[tex]\[-(20) = -20\][/tex]
3. Add 1:
[tex]\[-20 + 1 = -19\][/tex]
4. Therefore, [tex]\(-(9 + 11) + 1 = -19\)[/tex], not -1.
So, equation B is False.
Equation C: [tex]\(24 - (-6) - 6 = 24\)[/tex]
1. Start with the subtraction of a negative number (which is equivalent to adding):
[tex]\[24 - (-6) = 24 + 6 = 30\][/tex]
2. Now, subtract 6:
[tex]\[30 - 6 = 24\][/tex]
3. Therefore, [tex]\(24 - (-6) - 6 = 24\)[/tex].
So, equation C is True.
Equation D: [tex]\(12 + (-8) - 1 = 3\)[/tex]
1. Add -8 to 12:
[tex]\[12 + (-8) = 4\][/tex]
2. Then, subtract 1:
[tex]\[4 - 1 = 3\][/tex]
3. Therefore, [tex]\(12 + (-8) - 1 = 3\)[/tex].
So, equation D is True.
Equation E: [tex]\(-|2 - 7| + 5 = 0\)[/tex]
1. First, calculate the absolute value:
[tex]\[2 - 7 = -5\][/tex]
[tex]\[|-5| = 5\][/tex]
2. Apply the negative sign:
[tex]\[-|2 - 7| = -5\][/tex]
3. Add 5:
[tex]\[-5 + 5 = 0\][/tex]
4. Therefore, [tex]\(-|2 - 7| + 5 = 0\)[/tex].
So, equation E is True.
Based on the evaluations:
- Equation A: False
- Equation B: False
- Equation C: True
- Equation D: True
- Equation E: True
Here’s the final categorization:
A [tex]\(\square\)[/tex] False
B [tex]\(\square\)[/tex] False
C [tex]\(\square\)[/tex] True
D [tex]\(\square\)[/tex] True
E [tex]\(\square\)[/tex] True
