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Evaluate the following expressions and answer the question below:

[tex]\[
\begin{array}{l}
|-4 + 9| \\
|-4| + 9
\end{array}
\][/tex]

Which expression has the greater value?

A. [tex]\(|-4| + 9\)[/tex]

B. The expressions have the same value.

C. [tex]\(|-4 + 9|\)[/tex]

Sagot :

GinnyAnswer
Sure, let's evaluate the given expressions one by one and then compare their values.

### Step 1: Evaluate [tex]\(|-4 + 9|\)[/tex]

1.1 Compute the expression inside the absolute value:
[tex]\[ -4 + 9 = 5 \][/tex]

1.2 Take the absolute value:
[tex]\[ |5| = 5 \][/tex]

So, the value of the expression [tex]\(|-4 + 9|\)[/tex] is [tex]\(5\)[/tex].

### Step 2: Evaluate [tex]\(|-4| + 9\)[/tex]

2.1 Compute the absolute value of -4:
[tex]\[ |-4| = 4 \][/tex]

2.2 Add 9 to the result:
[tex]\[ 4 + 9 = 13 \][/tex]

So, the value of the expression [tex]\(|-4| + 9\)[/tex] is [tex]\(13\)[/tex].

### Step 3: Compare the results

We have:
[tex]\[ |-4 + 9| = 5 \][/tex]
[tex]\[ |-4| + 9 = 13 \][/tex]

Now, we compare these two values:

- The value of [tex]\(|-4 + 9|\)[/tex] is [tex]\(5\)[/tex].
- The value of [tex]\(|-4| + 9\)[/tex] is [tex]\(13\)[/tex].

Since [tex]\(13\)[/tex] is greater than [tex]\(5\)[/tex], the expression [tex]\(|-4| + 9\)[/tex] has the greater value.

### Conclusion

The expression [tex]\(|-4| + 9\)[/tex] has the greater value.
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