Determine whether each statement is true or false. |5+(-13) | = |5| + |-13|

Verified step by step guidance

1. Step 1: Understand the properties of absolute values. The absolute value of a number is its distance from zero on the number line, regardless of direction.
2. Step 2: Calculate the absolute value of the expression on the left side of the equation: \(|5 + (-13)|\).
3. Step 3: Simplify the expression inside the absolute value: \(5 + (-13) = -8\).
4. Step 4: Find the absolute value of \(-8\), which is \(|-8| = 8\).
5. Step 5: Calculate the absolute values on the right side of the equation: \(|5| = 5\) and \(|-13| = 13\), then add them together: \(5 + 13 = 18\).

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |5| equals 5, and |-13| equals 13. Absolute values are always non-negative.

Properties of Absolute Value

One important property of absolute values is that |a + b| ≤ |a| + |b|, known as the triangle inequality. This property indicates that the absolute value of a sum is less than or equal to the sum of the absolute values. Understanding this property is crucial for evaluating expressions involving absolute values.

Evaluating Expressions

To determine the truth of the statement, one must evaluate both sides of the equation. This involves calculating the absolute values and performing the arithmetic operations. For the given expression, evaluating |5 + (-13)| and |5| + |-13| will reveal whether the two sides are equal, thus confirming the statement's validity.