To solve the inequality $x + 8 \geq 14$, we can follow these steps:

Step 1: Isolate $x$

Subtract 8 from both sides of the inequality: $x + 8 - 8 \geq 14 - 8$ $x \geq 6$

Step 2: Interpret the solution

The solution is $x \geq 6$, meaning that $x$ can be any value greater than or equal to 6.

Step 3: Graph the solution on a number line

On a number line:

• Draw a solid circle at 6 (because the inequality is "greater than or equal to", so 6 is included in the solution set).
• Shade to the right of 6, indicating that any number greater than 6 is also a solution.

Here is a graphical representation:

<====●========================>
         6

Conclusion:

The solution set is $x \geq 6$, and the graph represents all values of $x$ from 6 onward.

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Would you like further details or explanations on any part of this? Here are some related questions you might find useful:

1. What if the inequality was $x + 8 < 14$?
2. How do you solve inequalities involving fractions?
3. What does it mean to solve an inequality "strictly" (without the "equal" part)?
4. How can you graph inequalities involving "less than" and "greater than" on a number line?
5. Can you solve and graph the inequality $2x + 4 \geq 12$?

Tip: When solving inequalities, always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.