To simplify the given expression [tex]\(\frac{3-4|2(-3)|}{|-3|}\)[/tex], we will proceed step-by-step through the calculation:
1. Calculate the absolute value of [tex]\(-3\)[/tex]:
[tex]\[
|-3| = 3
\][/tex]
2. Evaluate the inner absolute value:
[tex]\[
2(-3) = -6
\][/tex]
Then, take the absolute value of [tex]\(-6\)[/tex]:
[tex]\[
|-6| = 6
\][/tex]
3. Multiply 4 by the result of the inner absolute value:
[tex]\[
4 \cdot 6 = 24
\][/tex]
4. Compute the numerator by subtracting the above result from 3:
[tex]\[
3 - 24 = -21
\][/tex]
5. Using the result from step 1 as the denominator, we now have:
[tex]\[
\frac{-21}{3}
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
-21 \div 3 = -7
\][/tex]
Thus, the simplified expression is [tex]\(-7\)[/tex].
