Given inequality:

$x + 12 \leq 18$

Step 1: Solve for $x$

To isolate $x$, subtract 12 from both sides of the inequality:

$x + 12 - 12 \leq 18 - 12$

This simplifies to:

$x \leq 6$

So, the solution is:

$x \leq 6$

Step 2: Graph the solutions

The solution $x \leq 6$ means that $x$ can be any value less than or equal to 6. On a number line, we represent this by:

1. Drawing a solid circle at 6 (since $x$ can be equal to 6).
2. Shading the region to the left of 6 to show that all values less than or equal to 6 are included in the solution.

Number Line:

<---●========>
       6

The solid circle at 6 indicates that 6 is included in the solution, and the arrow to the left shows that all smaller numbers are also solutions.

Final Answer:

• The solution is $x \leq 6$.
• The graph shows a solid circle at 6 with shading to the left.

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Would you like to work through more inequalities or explore other types of equations?

Related Questions:

1. How would you graph the inequality $x > 3$?
2. What is the solution to $2x - 4 \geq 8$?
3. How do you solve and graph $5x + 10 < 25$?
4. What happens if the inequality is $x - 3 \leq 2$? How would you solve it?
5. If the inequality was $4x \geq 16$, what would the solution be?

Tip: When graphing inequalities, remember that a solid circle means "included" (≤ or ≥), while an open circle means "not included" (< or >)!