To find an equivalent form of the compound inequality 22 < 5x < 7, we need to isolate the variable x.
We can do this by dividing the entire inequality by 5. Remember, when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality signs, but since 5 is positive, we can divide without changing the signs:
22/5 < x < 7/5
This shows that x lies between 22/5 and 7/5. To express this in decimal form, we can calculate:
– 22/5 = 4.4
– 7/5 = 1.4
Thus, the equivalent form of the compound inequality in interval notation is (4.4, 1.4). However, since 4.4 is greater than 1.4, it actually indicates there are no solutions.
In conclusion, care must be taken while interpreting compound inequalities, especially in their contexts. Always simplify step-by-step, and check for the relationships between the bounds!