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

A.*x* < –9

B.*x* > 3

C.*x* < –3

D.*x* > 7


To solve the inequality \( 5(3 - x) < -2x + 6 \), follow these steps:

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

\[
5 \times 3 - 5 \times x = 15 - 5x
\]

So, the inequality becomes:

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

2. Move all the terms involving \( x \) to one side and the constants to the other side:

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

Simplify:

\[
15 - 3x < 6
\]

3. Subtract 15 from both sides:

\[
-3x < 6 - 15
\]

\[
-3x < -9
\]

4. Divide both sides by -3, and remember to reverse the inequality because you're dividing by a negative number:

\[
x > 3
\]

Thus, the correct inequality is \( x > 3 \), which corresponds to **Option B**.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you solve a system of linear inequalities?
4. What is the difference between a strict inequality and a non-strict inequality?
5. Can inequalities have infinite solutions?

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

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

Discover how to solve the inequality 5(3 – x) < –2x + 6 with a detailed step-by-step solution. This problem involves the distributive property, moving terms, and understanding the rules of inequalities. Suitable for students in Grades 8-10.

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