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To solve the inequality \( 35 > 5 - 5x \) using the addition and multiplication principles, follow these steps:

### Step 1: Isolate the term involving \( x \)
We begin by subtracting 5 from both sides of the inequality:
\[
35 - 5 > -5x
\]
This simplifies to:
\[
30 > -5x
\]

### Step 2: Solve for \( x \)
Next, divide both sides by -5. Remember, when dividing by a negative number in an inequality, we must reverse the inequality sign:
\[
\frac{30}{-5} < x
\]
\[
-6 < x
\]

Thus, the solution is:
\[
x > -6
\]

### Step 3: Interpret the solution
The solution set is all \( x \) values greater than \( -6 \). In interval notation, this is \( x > -6 \), which corresponds to answer choice **D** in the second image.

Would you like more details on any of the steps, or help with related concepts?

### Related Questions:
1. How do you solve inequalities with variables on both sides?
2. Why does dividing by a negative reverse the inequality sign?
3. How do you represent inequality solutions on a number line?
4. What is the difference between strict inequalities and inclusive inequalities?
5. Can you apply the same principles to compound inequalities?

### Tip:
Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Solve using the addition and multiplication principles: 35 > 5 - 5x

Learn how to solve the inequality 35 > 5 - 5x using the addition and multiplication principles. This step-by-step guide covers important concepts in algebra, such as reversing the inequality sign when dividing by a negative number. Suitable for Grades 7-10.

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