What does the inequality 3 < 7c < 4 mean?

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The inequality 3 < 7c < 4 presents a compound inequality that can be broken down into two separate parts. Let’s analyze what each part means and how we can solve for the variable c.

### Breaking Down the Inequality

This inequality essentially states that:

  • 7c > 3
  • 7c < 4

### Solving the Inequalities

Let’s solve each part for c.

1. **First Inequality: 7c > 3**

To isolate c, we divide both sides of the inequality by 7:

c > 3/7

2. **Second Inequality: 7c < 4**

Similarly, we divide both sides by 7:

c < 4/7

### Combining the Results

Now, we can combine the two results to find the range of c.

The final combined inequality is:

3/7 < c < 4/7

This indicates that the value of c must be greater than 3/7 but less than 4/7.

### Conclusion

In summary, the inequality 3 < 7c < 4 can be solved to show that c must lie in the interval (3/7, 4/7). When dealing with inequalities, it’s essential to follow the proper arithmetic operations while keeping in mind the direction of inequality signs.

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