Which inequality describes all solutions to 5(3 – x) < –2x + 6?
A.x > 7
B.x > 3
C.x < –9
D.x < –3

Let's solve the inequality step by step to determine which inequality describes all the solutions.

The inequality is:

\[
5(3 - x) < -2x + 6
\]

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

\[
5(3) - 5(x) < -2x + 6
\]

This simplifies to:

\[
15 - 5x < -2x + 6
\]

2. **Move all terms involving** \(x\) **to one side** by adding \(5x\) to both sides:

\[
15 < 3x + 6
\]

3. **Subtract 6** from both sides:

\[
9 < 3x
\]

4. **Solve for** \(x\) by dividing both sides by 3:

\[
x > 3
\]

So, the solution to the inequality is:

\[
x > 3
\]

Therefore, the correct answer is **B. \(x > 3\)**.

Would you like more details on any step? Here are 5 related questions:

1. How do you solve inequalities with variables on both sides?
2. What happens if you multiply or divide an inequality by a negative number?
3. How do inequalities differ from equations in their solutions?
4. Can you provide examples of compound inequalities?
5. How do absolute value inequalities work?

**Tip**: When solving inequalities, remember to reverse the inequality sign if you multiply or divide by a negative number.

Learn how to solve the inequality 5(3 - x) < -2x + 6 in a step-by-step process. This problem demonstrates key algebraic concepts such as distributing, moving terms, and solving inequalities. Ideal for students in Grades 8-10.

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