Pregunta
Determine which of the following points are included in the solution set to the following linear inequality, \[ 9 x+2 y<12 \] Answer 2 Points \( (0,0) \) \( (7,7) \) \( (2,-4) \) Prev \( (2,-3) \) \( (8,8) \)
Ask by Bond Bryant. in the United States
Jan 24,2025
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The points that satisfy the inequality \( 9x + 2y < 12 \) are \( (0, 0) \) and \( (2, -4) \).
Solución
To determine which points satisfy the inequality \( 9x + 2y < 12 \), substitute each point into the inequality:
1. **\( (0, 0) \)**:
\[
9(0) + 2(0) = 0 < 12 \quad \text{✓}
\]
2. **\( (7, 7) \)**:
\[
9(7) + 2(7) = 63 + 14 = 77 \not< 12 \quad \text{✗}
\]
3. **\( (2, -4) \)**:
\[
9(2) + 2(-4) = 18 - 8 = 10 < 12 \quad \text{✓}
\]
4. **\( (2, -3) \)**:
\[
9(2) + 2(-3) = 18 - 6 = 12 \not< 12 \quad \text{✗}
\]
5. **\( (8, 8) \)**:
\[
9(8) + 2(8) = 72 + 16 = 88 \not< 12 \quad \text{✗}
\]
**Points that satisfy the inequality:** \( (0, 0) \) and \( (2, -4) \).
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Let's check each point against the inequality \(9x + 2y < 12\): 1. For the point \( (0,0) \): \[ 9(0) + 2(0) = 0 < 12 \text{ (True)} \] 2. For the point \( (7,7) \): \[ 9(7) + 2(7) = 63 + 14 = 77 \not< 12 \text{ (False)} \] 3. For the point \( (2,-4) \): \[ 9(2) + 2(-4) = 18 - 8 = 10 < 12 \text{ (True)} \] 4. For the point \( (2,-3) \): \[ 9(2) + 2(-3) = 18 - 6 = 12 \not< 12 \text{ (False)} \] 5. For the point \( (8,8) \): \[ 9(8) + 2(8) = 72 + 16 = 88 \not< 12 \text{ (False)} \] Thus, the points included in the solution set are \( (0,0) \) and \( (2,-4) \).
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