Here are the steps to graph each inequality on a number line.
General Rules for Graphing:
*
Open Circle (○): Use this for $<$ (less than) or $>$ (greater than). It means the number is *not* included.
*
Closed Circle (●): Use this for $\le$ (less than or equal to) or $\ge$ (greater than or equal to). It means the number *is* included.
*
Shading Direction:
* If $x$ is
less than a number, shade to the
left.
* If $x$ is
greater than a number, shade to the
right.
---
1. $x < 1$
* The symbol is $<$, so we use an
open circle at 1.
* Since $x$ is less than 1, we shade to the
left.
2. $x \ge -6$
* The symbol is $\ge$, so we use a
closed circle at -6.
* Since $x$ is greater than -6, we shade to the
right.
3. $x \ge 4$
* The symbol is $\ge$, so we use a
closed circle at 4.
* Since $x$ is greater than 4, we shade to the
right.
4. $x \ge 8$
* The symbol is $\ge$, so we use a
closed circle at 8.
* Since $x$ is greater than 8, we shade to the
right.
5. $x \le 1$
* The symbol is $\le$, so we use a
closed circle at 1.
* Since $x$ is less than 1, we shade to the
left.
Final Answer:
1. Open circle at 1, shaded to the left.
2. Closed circle at -6, shaded to the right.
3. Closed circle at 4, shaded to the right.
4. Closed circle at 8, shaded to the right.
5. Closed circle at 1, shaded to the left.
Parent Tip: Review the logic above to help your child master the concept of solve and graph the inequalities worksheet answers.
