Linear Inequality C9C990

1. **State the problem:** We are given the inequality $$14x + 11y < -4$$ and need to understand its meaning and how to work with it. 2. **Understanding the inequality:** This is a linear inequality in two variables $$x$$ and $$y$$. It represents all points $$(x,y)$$ in the plane for which the expression $$14x + 11y$$ is less than $$-4$$. 3. **Rewrite the inequality:** To analyze it, we can isolate $$y$$: $$14x + 11y < -4$$ Subtract $$14x$$ from both sides: $$11y < -4 - 14x$$ Divide both sides by $$11$$ (positive number, so inequality direction stays the same): $$y < \frac{-4 - 14x}{11}$$ 4. **Interpretation:** The boundary line is $$y = \frac{-4 - 14x}{11}$$ and the inequality represents the half-plane below this line. 5. **Summary:** The solution set is all points $$(x,y)$$ such that $$y < \frac{-4 - 14x}{11}$$. This describes a region in the coordinate plane below the line $$14x + 11y = -4$$.