To solve the given inequality, [tex]\(-2x < -3(x - 5)\)[/tex], let's follow a step-by-step approach:
1. Distribute on the right side:
[tex]\[
-2x < -3(x - 5)
\][/tex]
Distribute the [tex]\(-3\)[/tex] across the terms inside the parentheses:
[tex]\[
-2x < -3x + 15
\][/tex]
2. Move all [tex]\(x\)[/tex] terms to one side:
To isolate [tex]\(x\)[/tex], add [tex]\(3x\)[/tex] to both sides of the inequality:
[tex]\[
-2x + 3x < -3x + 3x + 15
\][/tex]
Simplify the inequality:
[tex]\[
x < 15
\][/tex]
So, the inequality [tex]\(-2x < -3(x-5)\)[/tex] simplifies to [tex]\(x < 15\)[/tex].
Thus, the correct answer is:
B) [tex]\(x < 15\)[/tex]
