1. **Stating the problem:** We need to find the solution regions (daerah yang memenuhi) for the inequalities: 1. $x \leq 0$ 2. $x \geq 0$ 3. $y \leq 0$ 4. $y \geq 0$ 5. $x - y < 5$ 6. $-3x > 2y + 6$ 2. **Understanding inequalities and half-planes:** - Inequalities like $x \leq 0$ define half-planes on the coordinate plane. - The inequality $x - y < 5$ can be rewritten as $y > x - 5$ to understand the region above the line $y = x - 5$. - The inequality $-3x > 2y + 6$ can be rearranged to express $y$ in terms of $x$. 3. **Step-by-step solution:** **For 1. $x \leq 0$:** - This represents all points on the plane where the $x$-coordinate is less than or equal to zero. - It is the half-plane to the left of the $y$-axis including the $y$-axis. **For 2. $x \geq 0$:** - This represents all points where $x$ is greater than or equal to zero. - It is the half-plane to the right of the $y$-axis including the $y$-axis. **For 3. $y \leq 0$:** - All points where $y$ is less than or equal to zero. - The half-plane below the $x$-axis including the $x$-axis. **For 4. $y \geq 0$:** - All points where $y$ is greater than or equal to zero. - The half-plane above the $x$-axis including the $x$-axis. **For 5. $x - y < 5$:** - Rewrite as $y > x - 5$. - The boundary line is $y = x - 5$. - The solution region is the half-plane above this line (not including the line because of strict inequality). **For 6. $-3x > 2y + 6$:** - Rearrange: $$-3x > 2y + 6$$ $$-3x - 6 > 2y$$ $$\frac{-3x - 6}{2} > y$$ - So, $$y < \frac{-3x - 6}{2}$$ - The boundary line is $y = \frac{-3x - 6}{2}$. - The solution region is the half-plane below this line (not including the line because of strict inequality). 4. **Summary of solution regions:** - $x \leq 0$: Left half-plane including $y$-axis. - $x \geq 0$: Right half-plane including $y$-axis. - $y \leq 0$: Lower half-plane including $x$-axis. - $y \geq 0$: Upper half-plane including $x$-axis. - $x - y < 5$: Region above the line $y = x - 5$, excluding the line. - $-3x > 2y + 6$: Region below the line $y = \frac{-3x - 6}{2}$, excluding the line. These define the half-planes or regions on the coordinate plane that satisfy each inequality.