https://file.aiquickdraw.com/mathbot/file/1729536508088fwzu1k5o.jpg

The inequality provided in the image is:

\[
6x < 7x - 1 < 7 - 7x
\]

### Step-by-Step Solution:

This is a compound inequality, which means we have to break it into two separate inequalities and solve them individually.

1. **First part of the inequality:**
   \[
   6x < 7x - 1
   \]
   Subtract \(7x\) from both sides:
   \[
   6x - 7x < -1
   \]
   \[
   -x < -1
   \]
   Now, divide by \(-1\), but remember to flip the inequality:
   \[
   x > 1
   \]

2. **Second part of the inequality:**
   \[
   7x - 1 < 7 - 7x
   \]
   Add \(7x\) to both sides:
   \[
   14x - 1 < 7
   \]
   Add 1 to both sides:
   \[
   14x < 8
   \]
   Now, divide by 14:
   \[
   x < \frac{8}{14} = \frac{4}{7}
   \]

### Conclusion:

Combining the two results \(x > 1\) and \(x < \frac{4}{7}\) shows that there is **no solution**, because \(x\) cannot be both greater than 1 and less than \(\frac{4}{7}\) simultaneously.

Therefore, the solution to this inequality is the empty set.

Do you want more details or have any questions?

Here are 5 related questions:
1. What is a compound inequality and how is it different from simple inequalities?
2. How do we handle inequalities when dividing or multiplying by a negative number?
3. Can inequalities always be combined, or are there cases when they have no solution, like this one?
4. What is the significance of flipping inequality signs when multiplying or dividing?
5. How can graphing inequalities help in solving problems visually?

**Tip:** Always pay attention when dividing or multiplying both sides of an inequality by a negative number—this action reverses the inequality symbol.

Solve the inequality 6x < 7x - 1 < 7 - 7x.

This step-by-step guide explains how to solve the compound inequality 6x < 7x - 1 < 7 - 7x. It covers algebraic concepts such as basic inequality manipulation, flipping inequality signs when dividing by a negative, and combining results. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation