https://file.aiquickdraw.com/mathbot/file/1728666993222h78x0vwm.jpg

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!

Solve the following inequality symbolically: -2(x - 15) + 4 > 0

Learn how to solve the algebraic inequality -2(x - 15) + 4 > 0 with a detailed step-by-step explanation. This problem explores key algebraic concepts, including the distributive property and inequality manipulation. Suitable for students in Grades 8-10.

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