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When solving inequalities, our main goal is to isolate the variable on one side of the inequality sign. This process is similar to solving regular equations. Here's how you can do it:
First, identify the variable you want to isolate. In this case, it's the variable $$ z $$ from the inequality $$ z + 14 > 5 $$.
Next, perform the same operation on both sides of the inequality to keep the equation balanced.

Subtract 14 from both sides:
$$ z + 14 - 14 > 5 - 14 $$

This simplifies the inequality to:
$$ z > -9 $$
By isolating the variable, we have successfully found that $$ z $$ must be greater than -9 for the inequality to hold true.

One crucial aspect to consider when solving inequalities is the direction of the inequality sign. The inequality sign can be <, >, <=, or >=. In the given problem, the sign is >, meaning 'greater than'.

During mathematical operations, the direction of the inequality may change, especially when multiplying or dividing by a negative number. However, in our case, we are subtracting 14 from both sides. Since subtraction does not affect the direction of the inequality sign, the inequality sign remains the same.

This means, after isolating the variable, the direction of the inequality remains as >, leading to the final solution:
$$ z > -9 $$

Always double-check the direction of the inequality sign after performing operations to ensure accuracy.

When solving inequalities, the type of mathematical operation you perform can affect the outcome:

The four basic operations are addition, subtraction, multiplication, and division.

In the given exercise, we used subtraction to isolate the variable. Here are some rules to remember when performing operations with inequalities:
- Adding or subtracting the same number from both sides of the inequality keeps the direction of the inequality unchanged.
- Multiplying or dividing both sides by a positive number also keeps the direction unchanged.
- Multiplying or dividing both sides by a negative number reverses the direction of the inequality.
Therefore, understanding the types and effects of mathematical operations is essential for accurately solving inequalities. This knowledge helps ensure that the final inequality correctly reflects the relationship between the variable and the numbers involved.