Subjects algebra

Graph Inequality B305B5

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1. **State the problem:** Graph the inequality $x - y < -1$ on the coordinate plane with axes ranging from -10 to 10. 2. **Rewrite the inequality:** Start by isolating $y$. $$x - y < -1$$ Subtract $x$ from both sides: $$\cancel{x} - y < -1 - \cancel{x}$$ which simplifies to: $$-y < -1 - x$$ 3. **Divide both sides by $-1$ to solve for $y$.** Remember, dividing an inequality by a negative number reverses the inequality sign: $$\cancel{-1} \cdot y > \cancel{-1} \cdot (1 + x)$$ which gives: $$y > x + 1$$ 4. **Interpret the inequality:** The boundary line is $y = x + 1$. This line crosses the y-axis at $(0,1)$ and the x-axis at $(-1,0)$. 5. **Graph the boundary line:** Draw the line $y = x + 1$ as a dashed line because the inequality is strict ($>$), meaning points on the line are not included. 6. **Shade the solution region:** Since $y > x + 1$, shade the region above the line. **Final answer:** The graph is the region above the dashed line $y = x + 1$ on the coordinate plane from -10 to 10 on both axes.