To solve the inequality [tex]\( -4(2x - 1) > 5 - 3x \)[/tex], the first step is to distribute the [tex]\(-4\)[/tex] over the terms inside the parenthesis on the left side of the inequality.
Let's break it down:
1. Distribute -4 to the terms inside the parentheses:
[tex]\[
-4(2x - 1) = -4 \cdot 2x + (-4) \cdot (-1)
\][/tex]
When we distribute [tex]\(-4\)[/tex]:
[tex]\[
-4 \cdot 2x = -8x \quad \text{and} \quad -4 \cdot (-1) = 4
\][/tex]
2. Therefore, the left side of the inequality becomes:
[tex]\[
-8x + 4
\][/tex]
Thus, our inequality transforms to:
[tex]\[
-8x + 4 > 5 - 3x
\][/tex]
Accordingly, 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]
So, the correct answer is:
Distribute [tex]\(-4\)[/tex] to get [tex]\( -8x + 4 > 5 - 3x \)[/tex].
