I assume you want to solve the inequality that corresponds to the statement "The opposite of one-third a number is greater than 9". To do that, we can follow these steps:
- Let x be the number we are looking for.
- Translate the statement into an inequality using symbols. The opposite of a number means the negative of that number, and one-third of a number means multiplying that number by 1/3. So we get:
-x/3 > 9
- Solve the inequality by isolating x. To do that, we can multiply both sides by -3, which is the inverse operation of dividing by 3. But remember, when we multiply or divide by a negative number, we have to reverse the inequality sign. So we get:
x < -27
- Check the solution by plugging in a value for x that satisfies the inequality and see if it makes the statement true. For example, if x = -30, then -(-30)/3 = 10, which is greater than 9. So the solution is correct.
- Write the answer in words. The solution set is all the numbers that are less than -27.