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When working with inequalities like \(|y| > -10\), finding integer solutions involves picking numbers from the set of integers. Integers include all whole numbers, both positive and negative, as well as zero. Here are a few properties to remember about integers:

• They do not include fractions or decimals.
• They are a countable set, stretching infinitely in both the positive and negative directions.

To solve our inequality, we look for integer values that satisfy the condition given. Since any value of \(y\) results in an absolute value that is non-negative, we can confidently say all integers are solutions for \(|y| > -10\). Examples might include simple selections like \(-5, 0, 3, 7, 9\). Note the ease of selecting integers makes this task straightforward once the nature of absolute values in this context is understood.

Inequalities offer a way to express relationships between numbers that are not necessarily equal. An inequality like \(|y| > -10\) tells us there is a range of possible solutions rather than a single number. Here's what to know about inequalities:

• The inequality sign \(>\) means 'greater than'.
• Inequalities can show with \(>\) or \(<\) and their 'or equal to' counterparts, \(\geq\) and \(\leq\).

In the case of \(|y| > -10\), since absolute values are never negative, the inequality is always true. Thus, every integer is part of the solution set. Overall, this inequality is a special case where the restriction imposed by the inequality is trivial because of the properties of absolute values.

Non-negative values are numbers that are equal to or greater than zero. Absolute values, such as \(|y|\), fall under this category because they measure distance from zero, a concept that cannot be negative. Here’s what you should keep in mind about non-negative values:

• They include all positive numbers and zero.
• The only values excluded are negative numbers.

In our exercise, \(|y|\) as a non-negative entity, indicates that no matter the original value of \(y\), the resulting absolute value cannot be negative. Therefore, it is greater than \(-10\), reinforcing why every integer chosen serves as a solution.

The magnitude of a number is essentially its absolute value without focusing on sign. What does this mean?

• It quantifies how far a number is from zero on the number line.
• For instance, the magnitudes of \(-7\) and \(7\) are both \(7\).

By considering the inequality \(|y| > -10\), it becomes apparent that because magnitude is a non-negative measure, it surpasses any negative threshold like \(-10\). Hence, no restriction is placed on the integer solutions for \(y\). This understanding simplifies finding solutions, as attention need only be paid to various integer values themselves.