To solve the inequality [tex]\( -4(x + 7) < 3(x - 2) \)[/tex], follow these steps:
1. Distribute the constants on both sides of the inequality:
[tex]\[
-4(x + 7) < 3(x - 2)
\][/tex]
[tex]\[
-4x - 28 < 3x - 6
\][/tex]
2. Move the variable terms to one side by adding [tex]\(4x\)[/tex] to both sides:
[tex]\[
-28 < 3x - 6 + 4x
\][/tex]
[tex]\[
-28 < 7x - 6
\][/tex]
3. Move the constant term to the other side by adding [tex]\(6\)[/tex] to both sides:
[tex]\[
-28 + 6 < 7x
\][/tex]
[tex]\[
-22 < 7x
\][/tex]
4. Divide both sides by [tex]\(7\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{-22}{7} < x
\][/tex]
[tex]\[
x > \frac{-22}{7}
\][/tex]
5. Expressing it back in terms of an inequality with [tex]\(-7x\)[/tex]:
[tex]\[
-7x > 22
\][/tex]
Therefore, the correct inequality that is equivalent to the given inequality is:
[tex]\[
\boxed{ -7x > 22 }
\][/tex]
This matches option B.
