To solve the compound inequality 22 < 5x < 7 + 3, we first simplify the right side of the inequality. The expression 7 + 3 equals 10, so we can rewrite the original compound inequality as:
22 < 5x < 10
Next, we will separate this compound inequality into two parts to make it easier to solve:
- First part: 22 < 5x
- Second part: 5x < 10
Now, we will solve each part individually:
1. For the first part, 22 < 5x:
- To isolate x, we divide both sides of the inequality by 5:
- 22/5 < x
- This simplifies to approximately x > 4.4.
2. For the second part, 5x < 10:
- Again, we divide both sides by 5 to isolate x:
- x < 10/5
- This simplifies to x < 2.
Now we can combine the results of both parts to express our solution:
4.4 < x < 2
This indicates that the compound inequality restricts x to values between roughly 4.4 and 2. However, we realize there’s a contradiction since 4.4 is greater than 2, which means there are no possible values for x that satisfy this inequality simultaneously.
Therefore, the original compound inequality 22 < 5x < 10 does not have an equivalent solution set, as indicated by:
No solution.