Printable math worksheet for solving and graphing inequalities, featuring eight problems with number lines.

Here are the step-by-step solutions for each inequality problem.

1) $x - 2 > 4$
* Solve: Add 2 to both sides.
$$x > 4 + 2$$
$$x > 6$$
* Graph: Draw an open circle at 6 (because it is strictly greater than, not equal to). Shade the line to the right.

2) $\frac{x}{3} \leq 7$
* Solve: Multiply both sides by 3.
$$x \leq 7 \times 3$$
$$x \leq 21$$
* Graph: Draw a closed (filled) circle at 21 (because of the "or equal to" part). Shade the line to the left.

3) $6x < 30$
* Solve: Divide both sides by 6.
$$x < \frac{30}{6}$$
$$x < 5$$
* Graph: Draw an open circle at 5. Shade the line to the left.

4) $x + 9 \geq 11$
* Solve: Subtract 9 from both sides.
$$x \geq 11 - 9$$
$$x \geq 2$$
* Graph: Draw a closed (filled) circle at 2. Shade the line to the right.

5) $\frac{x}{2} \geq 10$
* Solve: Multiply both sides by 2.
$$x \geq 10 \times 2$$
$$x \geq 20$$
* Graph: Draw a closed (filled) circle at 20. Shade the line to the right.

6) $x - 5 \leq 2$
* Solve: Add 5 to both sides.
$$x \leq 2 + 5$$
$$x \leq 7$$
* Graph: Draw a closed (filled) circle at 7. Shade the line to the left.

7) $7 + x < 16$
* Solve: Subtract 7 from both sides.
$$x < 16 - 7$$
$$x < 9$$
* Graph: Draw an open circle at 9. Shade the line to the left.

8) $4x \geq 32$
* Solve: Divide both sides by 4.
$$x \geq \frac{32}{4}$$
$$x \geq 8$$
* Graph: Draw a closed (filled) circle at 8. Shade the line to the right.

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Final Answer:
1) $x > 6$ (Open circle at 6, shade right)
2) $x \leq 21$ (Closed circle at 21, shade left)
3) $x < 5$ (Open circle at 5, shade left)
4) $x \geq 2$ (Closed circle at 2, shade right)
5) $x \geq 20$ (Closed circle at 20, shade right)
6) $x \leq 7$ (Closed circle at 7, shade left)
7) $x < 9$ (Open circle at 9, shade left)
8) $x \geq 8$ (Closed circle at 8, shade right)