Write each statement using an absolute value equation or inequality. p is at least 3 units from 1.

Verified step by step guidance

1. Understand that the phrase 'at least 3 units from 1' means the distance between \( p \) and 1 is 3 or more.
2. Recall that the absolute value \( |x - a| \) represents the distance between \( x \) and \( a \) on the number line.
3. Set up the inequality to represent the distance: \(|p - 1| \geq 3\).
4. This inequality states that the distance between \( p \) and 1 is greater than or equal to 3.
5. The solution to this inequality will give the values of \( p \) that are at least 3 units away from 1.

Key Concepts

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, which equals x if x is positive or zero, and -x if x is negative. Understanding absolute value is crucial for solving equations and inequalities that involve distance.

Inequalities

Inequalities express a relationship where one quantity is larger or smaller than another, using symbols like >, <, ≥, or ≤. In the context of absolute value, inequalities can describe conditions where a variable must be a certain distance from a point, which is essential for interpreting statements about distance.

Distance from a Point

The concept of distance from a point on the number line is fundamental in absolute value equations and inequalities. When a statement specifies that a variable is 'at least' a certain distance from a point, it translates into an absolute value expression that captures both directions from that point, allowing for a complete representation of the condition.