To solve the inequality [tex]\(-4(2x - 1) > 5 - 3x\)[/tex], we need to manipulate it correctly by following the right steps.
Let's examine the choices provided:
1. Distribute [tex]\(-4\)[/tex] to get [tex]\(-8x + 4 > 5 - 3x\)[/tex].
2. Distribute [tex]\(-4\)[/tex] to get [tex]\(-8x - 1 > 5 - 3x\)[/tex].
3. Subtract [tex]\(2x\)[/tex] from both sides of the inequality.
4. Add 1 to both sides of the inequality.
Among these steps, the correct initial step is to distribute [tex]\(-4\)[/tex] to the terms inside the parentheses. Let's carefully check the distribution:
- Distributing [tex]\(-4\)[/tex] to [tex]\((2x - 1)\)[/tex] inside the parentheses:
[tex]\[
-4(2x) = -8x
\][/tex]
[tex]\[
-4(-1) = +4
\][/tex]
So, the result of distributing [tex]\(-4\)[/tex] to [tex]\((2x - 1)\)[/tex] is:
[tex]\[
-8x + 4
\][/tex]
Therefore, the inequality becomes:
[tex]\[
-8x + 4 > 5 - 3x
\][/tex]
Thus, the correct first step in solving the inequality is:
[tex]\[
\text{Distribute } -4 \text{ to get } -8x + 4 > 5 - 3x.
\][/tex]
This aligns with option 1.
