To solve the inequality $5(3 - x) < -2x + 6$, follow these steps:

1. Distribute the 5 on the left-hand side:

$5 \times 3 - 5 \times x = 15 - 5x$

So, the inequality becomes:

$15 - 5x < -2x + 6$

2. Move all the terms involving $x$ to one side and the constants to the other side:

$15 - 5x + 2x < 6$

Simplify:

$15 - 3x < 6$

3. Subtract 15 from both sides:

$-3x < 6 - 15$

$-3x < -9$

4. Divide both sides by -3, and remember to reverse the inequality because you're dividing by a negative number:

$x > 3$

Thus, the correct inequality is $x > 3$, which corresponds to Option B.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you solve a system of linear inequalities?
4. What is the difference between a strict inequality and a non-strict inequality?
5. Can inequalities have infinite solutions?

Tip: Always remember to reverse the inequality sign when dividing or multiplying by a negative number!