To solve the inequality [tex]\(-4(2x-1) > 5 - 3x\)[/tex], follow these steps:
1. Distribute [tex]\(-4\)[/tex] across the terms inside the parentheses on the left side of the inequality.
This step involves multiplying [tex]\(-4\)[/tex] by each term inside the parentheses:
[tex]\[
-4(2x - 1) = -4 \cdot 2x + (-4) \cdot (-1)
\][/tex]
2. Performing the multiplications leads to:
[tex]\[
-4 \cdot 2x = -8x \quad \text{and} \quad -4 \cdot -1 = 4
\][/tex]
3. Therefore, the inequality after distribution looks like this:
[tex]\[
-8x + 4 > 5 - 3x
\][/tex]
Hence, the correct first step in solving the inequality [tex]\(-4(2x-1) > 5 - 3x\)[/tex] is to:
Distribute [tex]\(-4\)[/tex] to get [tex]\(-8x + 4 > 5 - 3x\)[/tex].
