Let's simplify the expression [tex]\( 3|-(6-4)| + 2|1+3| \)[/tex] step by step.
First, we evaluate the absolute values inside the expression:
1. Evaluate [tex]\( 6 - 4 \)[/tex]:
[tex]\[
6 - 4 = 2
\][/tex]
Then, find the absolute value of [tex]\(-2\)[/tex]:
[tex]\[
|-(6-4)| = |-2| = 2
\][/tex]
2. Evaluate [tex]\( 1 + 3 \)[/tex]:
[tex]\[
1 + 3 = 4
\][/tex]
Then, find the absolute value of [tex]\( 4 \)[/tex]:
[tex]\[
|1 + 3| = |4| = 4
\][/tex]
Now, substitute these absolute values back into the expression:
[tex]\[
3|-(6-4)| + 2|1+3| = 3 \cdot 2 + 2 \cdot 4
\][/tex]
Next, we perform the multiplications:
[tex]\[
3 \cdot 2 = 6
\][/tex]
[tex]\[
2 \cdot 4 = 8
\][/tex]
Finally, add the results:
[tex]\[
6 + 8 = 14
\][/tex]
So, the simplified value of the expression [tex]\( 3|-(6-4)| + 2|1+3| \)[/tex] is:
[tex]\[
\boxed{14}
\][/tex]
