Write each statement using an absolute value equation or inequality.
m is no more than 2 units from 7.

Verified step by step guidance

1. Identify the key phrase "no more than 2 units from 7," which means the distance between m and 7 is at most 2.
2. Recall that the absolute value expression \$|m - 7|\$ represents the distance between m and 7 on the number line.
3. Translate "no more than 2 units" into an inequality: the distance is less than or equal to 2, so write \$|m - 7| \leq 2\$.
4. Write the absolute value inequality that represents the statement: \$|m - 7| \leq 2\$.
5. This inequality means m is within 2 units of 7, including the points exactly 2 units away.

Key Concepts

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. It is denoted by |x| and measures magnitude without regard to direction, which is essential for expressing distance-related problems.

Distance on the Number Line

Distance between two points on the number line is the absolute value of their difference. For example, the distance between m and 7 is |m - 7|, which helps translate verbal statements about proximity into mathematical expressions.

Inequalities Involving Absolute Value

An inequality with absolute value, such as |x - a| ≤ b, describes all values x within b units of a. This concept is used to express conditions like 'no more than' or 'within a certain distance' from a point, crucial for writing the given statement as an inequality.