Let's solve the inequality step by step.

We are given the inequality:

$-2(x - 15) + 4 > 0$

Step 1: Distribute the $-2$ across the terms inside the parentheses:

$-2(x - 15) = -2x + 30$ So the inequality becomes: $-2x + 30 + 4 > 0$

Step 2: Combine like terms:

$-2x + 34 > 0$

Step 3: Isolate the variable $x$:

Subtract 34 from both sides: $-2x > -34$

Step 4: Divide by $-2$:

Remember, when dividing an inequality by a negative number, we reverse the inequality sign. $x < 17$

Solution:

The solution in interval notation is: $(-\infty, 17)$

Would you like further details or have any questions?

Related Questions:

1. How would the solution change if the inequality were $-2(x - 15) + 4 \geq 0$?
2. What if the inequality involved $-3(x - 15) + 4 > 0$?
3. How can inequalities be represented graphically?
4. How does the solution change if the inequality had a positive multiplier, e.g., $2(x - 15) + 4 > 0$?
5. How do you solve compound inequalities with two inequality signs?

Tip:

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