Question

Select the number line model that matches the expression [|4 - 1|].

1) [|-3|]
2) [|-2|]
3) [|-1|]
4) [|3 - 1|]

Answer 1

The expression [|4 - 1|] simplifies to [3]. The matching number line model is option 1, [|-3|], which becomes [3] after applying the absolute value.

Step-by-step explanation:

The question involves finding which number line model matches the expression [|4 - 1|]. To begin, we must calculate the value inside the absolute value symbol: 4 - 1 equals 3. Now, the expression becomes [|3|], which simplifies to 3 because the absolute value of 3 is 3. Therefore, we need to find the number line model that represents the number 3 after applying absolute value.

Looking at the options provided:

1. [|-3|] which becomes [3] after taking absolute value.
2. [|-2|] which becomes [2] after taking absolute value.
3. [|-1|] which becomes [1] after taking absolute value.
4. [|3 - 1|] which becomes [2] after performing 3 - 1 and then taking the absolute value.

From the options listed, option 1 is the correct one since it matches our initial calculation of [|4 - 1|] which is [3]. Remember that the absolute value of a number is the distance from zero on a number line, always a positive value, or zero.