Which inequality describes all solutions to 5(3 – x) < –2x + 6?

We are given the inequality \( 5(3 - x) < -2x + 6 \). Let's solve it step by step:

### Step 1: Distribute the 5 on the left side.
\[
5 \cdot 3 - 5 \cdot x = 15 - 5x
\]
So the inequality becomes:
\[
15 - 5x < -2x + 6
\]

### Step 2: Move all the terms with \(x\) to one side.
Add \(5x\) to both sides to eliminate the \( -5x \) on the left:
\[
15 < 3x + 6
\]

### Step 3: Move the constants to the other side.
Subtract 6 from both sides:
\[
15 - 6 < 3x
\]
\[
9 < 3x
\]

### Step 4: Solve for \(x\).
Divide both sides by 3:
\[
x > 3
\]

Thus, the inequality describing all solutions is:
\[
x > 3
\]

Would you like any details or further explanation on any part of this solution?

Here are 5 follow-up questions to consider:
1. How do you check if a value is a solution to an inequality?
2. What is the difference between solving inequalities and equations?
3. How would the solution change if the inequality sign was reversed?
4. How do you graph the solution \(x > 3\) on a number line?
5. What happens if you multiply or divide both sides of an inequality by a negative number?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number flips the inequality sign!

This page provides a detailed step-by-step solution for solving the inequality 5(3 – x) < –2x + 6. Learn how to apply the distributive property, move terms across the inequality, and solve for x. Perfect for students in Grades 7-9 learning about inequalities in algebra.

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