Answer :
To solve this problem, we need to analyze each row and compare the solutions for [tex]\(x\)[/tex] in column A and [tex]\(y\)[/tex] in column B step by step:
1. Row 1:
- Equation in column A: [tex]\(11x + 2 = 6\)[/tex]
[tex]\[ 11x = 6 - 2 \][/tex]
[tex]\[ 11x = 4 \][/tex]
[tex]\[ x = \frac{4}{11} \approx 0.36 \][/tex]
- Equation in column B: [tex]\(y - 4 = -6\)[/tex]
[tex]\[ y = -6 + 4 \][/tex]
[tex]\[ y = -2 \][/tex]
- Comparison: Column A ([tex]\(0.36\)[/tex]) is greater than Column B ([tex]\(-2\)[/tex])
2. Row 2:
- Equation in column A: [tex]\(12x + |-3| = 3\)[/tex]
[tex]\[ 12x + 3 = 3 \][/tex]
[tex]\[ 12x = 0 \][/tex]
[tex]\[ x = 0 \][/tex]
- Equation in column B: [tex]\(6 = y + 4\)[/tex]
[tex]\[ y = 6 - 4 \][/tex]
[tex]\[ y = 2 \][/tex]
- Comparison: Column A ([tex]\(0\)[/tex]) is less than Column B ([tex]\(2\)[/tex])
3. Row 3:
- Equation in column A: [tex]\(|x| - 2 = 6\)[/tex]
[tex]\[ |x| = 6 + 2 \][/tex]
[tex]\[ |x| = 8 \][/tex]
[tex]\[ x = \pm 8 \][/tex]
- Equation in column B: [tex]\(y - 3 = 4\)[/tex]
[tex]\[ y = 4 + 3 \][/tex]
[tex]\[ y = 7 \][/tex]
- Comparison: For [tex]\(x = 8\)[/tex], Column A ([tex]\(8\)[/tex]) is greater than Column B ([tex]\(7\)[/tex]). For [tex]\(x = -8\)[/tex], Column A ([tex]\(-8\)[/tex]) is less than Column B ([tex]\(7\)[/tex])
4. Row 4:
- Equation in column A: [tex]\(-6 - x = 3\)[/tex]
[tex]\[ -x = 3 + 6 \][/tex]
[tex]\[ -x = 9 \][/tex]
[tex]\[ x = -9 \][/tex]
- Equation in column B: [tex]\(-2 = y - (-8)\)[/tex]
[tex]\[ -2 = y + 8 \][/tex]
[tex]\[ y = -2 - 8 \][/tex]
[tex]\[ y = -10 \][/tex]
- Comparison: Column A ([tex]\(-9\)[/tex]) is greater than Column B ([tex]\(-10\)[/tex])
Based on these comparisons, the answers for each row are:
- Row 1: Column A solution is greater
- Row 2: Column B solution is greater
- Row 3: Both comparisons:
- [tex]\(x = 8\)[/tex]: Column A solution is greater
- [tex]\(x = -8\)[/tex]: Column B solution is greater
- Row 4: Column A solution is greater
So, summarizing:
- Row 1: Column A is greater
- Row 2: Column B is greater
- Row 3: The relationship cannot be determined (depends on the sign of [tex]\(x\)[/tex])
- Row 4: Column A is greater
1. Row 1:
- Equation in column A: [tex]\(11x + 2 = 6\)[/tex]
[tex]\[ 11x = 6 - 2 \][/tex]
[tex]\[ 11x = 4 \][/tex]
[tex]\[ x = \frac{4}{11} \approx 0.36 \][/tex]
- Equation in column B: [tex]\(y - 4 = -6\)[/tex]
[tex]\[ y = -6 + 4 \][/tex]
[tex]\[ y = -2 \][/tex]
- Comparison: Column A ([tex]\(0.36\)[/tex]) is greater than Column B ([tex]\(-2\)[/tex])
2. Row 2:
- Equation in column A: [tex]\(12x + |-3| = 3\)[/tex]
[tex]\[ 12x + 3 = 3 \][/tex]
[tex]\[ 12x = 0 \][/tex]
[tex]\[ x = 0 \][/tex]
- Equation in column B: [tex]\(6 = y + 4\)[/tex]
[tex]\[ y = 6 - 4 \][/tex]
[tex]\[ y = 2 \][/tex]
- Comparison: Column A ([tex]\(0\)[/tex]) is less than Column B ([tex]\(2\)[/tex])
3. Row 3:
- Equation in column A: [tex]\(|x| - 2 = 6\)[/tex]
[tex]\[ |x| = 6 + 2 \][/tex]
[tex]\[ |x| = 8 \][/tex]
[tex]\[ x = \pm 8 \][/tex]
- Equation in column B: [tex]\(y - 3 = 4\)[/tex]
[tex]\[ y = 4 + 3 \][/tex]
[tex]\[ y = 7 \][/tex]
- Comparison: For [tex]\(x = 8\)[/tex], Column A ([tex]\(8\)[/tex]) is greater than Column B ([tex]\(7\)[/tex]). For [tex]\(x = -8\)[/tex], Column A ([tex]\(-8\)[/tex]) is less than Column B ([tex]\(7\)[/tex])
4. Row 4:
- Equation in column A: [tex]\(-6 - x = 3\)[/tex]
[tex]\[ -x = 3 + 6 \][/tex]
[tex]\[ -x = 9 \][/tex]
[tex]\[ x = -9 \][/tex]
- Equation in column B: [tex]\(-2 = y - (-8)\)[/tex]
[tex]\[ -2 = y + 8 \][/tex]
[tex]\[ y = -2 - 8 \][/tex]
[tex]\[ y = -10 \][/tex]
- Comparison: Column A ([tex]\(-9\)[/tex]) is greater than Column B ([tex]\(-10\)[/tex])
Based on these comparisons, the answers for each row are:
- Row 1: Column A solution is greater
- Row 2: Column B solution is greater
- Row 3: Both comparisons:
- [tex]\(x = 8\)[/tex]: Column A solution is greater
- [tex]\(x = -8\)[/tex]: Column B solution is greater
- Row 4: Column A solution is greater
So, summarizing:
- Row 1: Column A is greater
- Row 2: Column B is greater
- Row 3: The relationship cannot be determined (depends on the sign of [tex]\(x\)[/tex])
- Row 4: Column A is greater
