Which is a correct first step in solving the inequality [tex]-4(2x-1) \ \textgreater \ 5 - 3x[/tex]?

A. Distribute -4 to get [tex]-8x + 4 \ \textgreater \ 5 - 3x[/tex].
B. Distribute -4 to get [tex]-8x - 1 \ \textgreater \ 5 - 3x[/tex].
C. Subtract [tex]2x[/tex] from both sides of the inequality.
D. Add 1 to both sides of the inequality.



Answer :

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.