Question

Describe the error
3x-5y≤-5

Answer 1

The inequality \( 3x - 5y \leq -5 \) does not contain any mathematical error; it is a valid linear inequality in two variables, \(x\) and \(y\). However, if you're looking for a description or interpretation, here's how it can be analyzed:

1. **Linear Inequality Representation**: This inequality represents a region in the coordinate plane. The left side of the inequality \(3x - 5y\) represents a linear equation when set as an equality \(3x - 5y = -5\). The solution to this equation is a line.

2. **Graphing the Inequality**:
- First, you would graph the line \(3x - 5y = -5\). To do this, you can find the intercepts:
- For the x-intercept (where \(y=0\)):
\[
3x = -5 \implies x = -\frac{5}{3}
\]
- For the y-intercept (where \(x=0\)):
\[
-5y = -5 \implies y = 1
\]

- So, the points \((-5/3, 0)\) and \((0, 1)\) are on the line.

- Next, you need to determine the region satisfying \(3x - 5y \leq -5\). Since the inequality is "less than or equal to," you would shade the area below the line, including the line itself (since it's "or equal to").

3. **Solution Set**: The solution set consists of all points \((x,y)\) that satisfy the inequality \(3x - 5y \leq -5\). This set represents a half-plane in the Cartesian coordinate system.

If there is a specific error or context you are referring to (e.g., in the application of the inequality, a misinterpretation involving it, etc.), please provide more details!