The expression "3x - 2y ≥ 8" represents a linear inequality rather than an error. It defines a region in a two-dimensional space (the coordinate plane) where the relationship between the variables \(x\) and \(y\) holds true.
To analyze this inequality:
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Identify the equation: First, rewrite the inequality as an equation: \[ 3x - 2y = 8 \] This is the boundary line of the inequality.
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Graph the line: To graph this line, find where it intersects the axes:
- When \(x = 0\): \[ -2y = 8 \implies y = -4 \quad \text{(y-intercept)} \]
- When \(y = 0\): \[ 3x = 8 \implies x = \frac{8}{3} \quad \text{(x-intercept)} \]
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Determine the shading: The inequality \(3x - 2y ≥ 8\) means you want to include the line itself (since it's a "greater than or equal to" sign). The solution region will be above the line because you are looking for values where the expression \(3x - 2y\) is greater than or equal to 8.
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Test a point: To confirm which side of the line to shade, you can test a point not on the line, such as \((0, 0)\): \[ 3(0) - 2(0) ≥ 8 \implies 0 ≥ 8 \quad \text{(false)} \] Since this test point does not satisfy the inequality, you will shade the area above the line where values of \(3x - 2y\) are greater than or equal to 8.
In summary, "3x - 2y ≥ 8" is a mathematical representation of a region in the plane, not an error. If you intended something else regarding the context of "error," please clarify for further assistance!