Question

evaluate the following.
(a)
( left| 5 - 7
ight| = )
(b)
( left| 5 - 7
ight| = )

Explanation:

Step1: Evaluate |5 - 7|

First, calculate the expression inside the absolute value: \(5 - 7 = -2\). Then, the absolute value of \(-2\) is \(|-2| = 2\). Wait, no, wait, the first part (a) is \(|5| - 7\)? Wait, no, looking at the image, (a) is \(|5| - 7\)? Wait, no, the notation: (a) is \(|5| - 7\)? Wait, no, the original problem: (a) is \(|5| - 7\)? Wait, no, the user's image: (a) is \(|5| - 7\)? Wait, no, let's re-examine. Wait, the first one (a) is \(|5| - 7\)? Wait, no, the vertical bars: (a) is \(|5| - 7\)? Wait, no, maybe (a) is \(|5 - 7|\)? Wait, no, the way it's written: (a) is \(|5| - 7\)? Wait, no, the image shows (a) as \(|5| - 7 =\) and (b) as \(|5 - 7| =\). Wait, let's correct:

Step1: Evaluate (a) \(|5| - 7\)

The absolute value of 5 is \(|5| = 5\). Then subtract 7: \(5 - 7 = -2\).

Step2: Evaluate (b) \(|5 - 7|\)

First, calculate inside the absolute value: \(5 - 7 = -2\). Then take the absolute value: \(|-2| = 2\).

Wait, but the user's problem: let's check again. The image says:

(a) \(|5| - 7 =\) (wait, no, maybe the vertical bars are around 5 - 7? Wait, the original image: (a) is \(|5 - 7| =\)? Wait, no, the way it's typeset: (a) is \(|5| - 7\)? No, the vertical bars: (a) is \(|5 - 7|\)? Wait, the user's image: (a) is \(|5| - 7\)? No, let's look at the numbers: 5, then a vertical bar, then -7? No, maybe the first one (a) is \(|5| - 7\), and (b) is \(|5 - 7|\). Let's proceed:

For (a): \(|5| = 5\), so \(5 - 7 = -2\).

For (b): \(5 - 7 = -2\), \(|-2| = 2\).

But the user's problem: let's confirm the notation. The image shows (a) as \(|5| - 7\) (with vertical bar around 5) and (b) as \(|5 - 7|\) (vertical bar around 5 - 7).

So:

(a) \(|5| - 7 = 5 - 7 = -2\)

(b) \(|5 - 7| = |-2| = 2\)

But the user's question: maybe the first part (a) is \(|5 - 7|\)? Wait, no, the way it's written: (a) is \(|5| - 7\) (vertical bar around 5) and (b) is \(|5 - 7|\) (vertical bar around 5 - 7). Let's solve both:

(a) \(|5| - 7 = 5 - 7 = -2\)

(b) \(|5 - 7| = |-2| = 2\)

But the user's problem: the first box (a) is already filled? No, the user's image: (a) has a filled box, (b) is empty. Wait, no, the user's question: maybe the problem is to evaluate (a) and (b). Wait, the user's instruction: "Evaluate the following." with (a) and (b). Let's assume (a) is \(|5 - 7|\) (maybe a typo in the image). Wait, no, let's check the numbers: 5, -, 7, with vertical bars. So (a) is \(|5 - 7|\)? No, the vertical bars: (a) is \(|5| - 7\), (b) is \(|5 - 7|\).

But let's proceed with the correct absolute value operations.

For (b): \(|5 - 7| = |-2| = 2\).

So the answer for (b) is 2.

Answer:

For (a): \(-2\) (if \(|5| - 7\)), for (b): \(2\) (if \(|5 - 7|\)). But based on the image, (b) is \(|5 - 7| =\), so the answer is \(2\).