To solve the inequality \(7x - 1 \leq 2x - 8\), follow these steps:

1. **Move all terms involving \(x\) to one side of the inequality**:
   \[
   7x - 2x \leq -8 + 1
   \]
   Simplifying:
   \[
   5x \leq -7
   \]

2. **Solve for \(x\)** by dividing both sides by 5:
   \[
   x \leq \frac{-7}{5}
   \]
   \[
   x \leq -\frac{7}{5}
   \]

Thus, the solution is:
\[
x \leq -\frac{7}{5}
\]

Would you like any further details or clarifications?

Here are five related questions to deepen your understanding:
1. How would the solution change if the inequality were \(7x - 1 \geq 2x - 8\)?
2. Can you graph the inequality \(7x - 1 \leq 2x - 8\) on a number line?
3. How does the solution differ if it was a strict inequality \(7x - 1 < 2x - 8\)?
4. What is the impact of multiplying or dividing both sides of an inequality by a negative number?
5. How can inequalities be used in real-world applications, like budgeting or planning?

**Tip:** Always reverse the inequality sign when multiplying or dividing by a negative number in inequalities.

Explore how to solve the linear inequality 7x - 1 ≤ 2x - 8 with a step-by-step guide. This problem introduces essential concepts in algebra, including solving inequalities and properties of linear equations. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation