Problem 82

Question

Determine whether each statement is true or false. $-|12|>|-15|$

Step-by-Step Solution

Verified

Answer

True

1Step 1: Evaluate the Absolute Value

Calculate the absolute value of 12. Since $|12| = 12$, the expression becomes $-12$.

2Step 2: Simplify the Right-Hand Side

The right-hand side of the inequality is $-15$.

3Step 3: Compare the Values

Now compare $-12$ and $-15$. Since $-12$ is greater than $-15$, the statement $-|12| > -15$ is true.

Key Concepts

absolute valueinequalitynegative numbers

absolute value

The absolute value of a number is its distance from zero on a number line, regardless of direction. To find the absolute value, you simply disregard the sign.
For example:

The absolute value of 12 is $|12| = 12$ since it's 12 units away from zero.
Likewise, the absolute value of -12 is $|-12| = 12$.

Absolute value turns all numbers into non-negative values. This concept is essential in mathematics, especially when dealing with distances and magnitudes.

inequality

Inequality compares two values, showing if one is less than, greater than, or equal to another. In mathematical notation:

$a < b$ means 'a' is less than 'b'.
$a > b$ means 'a' is greater than 'b'.
$a \leq b$ means 'a' is less than or equal to 'b'.
$a \geq b$ means 'a' is greater than or equal to 'b'.

In our example, we used the inequality $-|12| > -15$. We simplified the left side to $-12$ and then compared $-12$ with $-15$. Since $-12$ is indeed greater than $-15$, the inequality holds true.