What is the absolute value of the expression $|-254|-|-125|+|17|$?

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03-11-2026
Mathematics

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What is the absolute value of the expression $|-254|-|-125|+|17|$?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T21:09:27-05:00

Evaluate each absolute value term: $|-254| = 254$, $|-125| = 125$, and $|17| = 17$.
Substitute these values into the expression to get $254 - 125 + 17$.
Perform the arithmetic to obtain $146$.
The absolute value of the final expression is $|146| = \boxed{146}$.

Explanation

Understanding Absolute Value

We are given the expression $|-254| - |-125| + |17|$. To solve this, we first need to recall the definition of the absolute value of a real number $x$, denoted by $|x|$. The absolute value $|x|$ is the distance of the number $x$ from zero on the number line. Specifically, $|x| = x$ if $x \ge 0$, and $|x| = -x$ if $x < 0$. This means that for any real number, the absolute value is always non-negative.

Evaluating the Absolute Value Terms

Now, let us compute the value of each term individually based on the definition of absolute value:

For $|-254|$, since $-254 < 0$, we have $|-254| = -(-254) = 254$.
For $|-125|$, since $-125 < 0$, we have $|-125| = -(-125) = 125$.
For $|17|$, since $17 \ge 0$, we have $|17| = 17$.

Substituting these back into our original expression, we get:
\[254 - 125 + 17\]

Computing the Final Result

With the terms evaluated, we perform the arithmetic operations:

First, subtract 125 from 254: $254 - 125 = 129$.
Next, add 17: $129 + 17 = 146$.

The problem asks for the absolute value of this entire expression:
\[|254 - 125 + 17| = |146|\]
Since $146 > 0$, the absolute value is simply 146.

Examples

Absolute values are used in various fields to measure magnitude regardless of direction. For instance, in finance, if you track your daily balance relative to a baseline, an absolute value helps determine the total deviation from that baseline, whether your balance went up or down. Similarly, in physics, it is used to measure speed, which is the magnitude of velocity regardless of the direction of movement. This allows scientists and accountants to focus on the scale of a change rather than just its sign.