Final answer:
The solution involves solving the inequality -36 < 2x - 6 < 40 to find that the possible values for the variable are greater than -15 and less than 23.
Step-by-step explanation:
The question asks us to represent an inequality involving a variable and solve for its possible values such that two times a number decreased by six is between -36 and 40. We can set this up as an inequality: -36 < 2x - 6 < 40. To solve for x, we must isolate the variable.
- Add 6 to all three parts of the inequality: -36 + 6 < 2x - 6 + 6 < 40 + 6, which simplifies to -30 < 2x < 46.
- Divide all three parts by 2 to solve for x: -30/2 < 2x/2 < 46/2, which results in -15 < x < 23.
Therefore, the number x must be greater than -15 and less than 23 to satisfy the given inequality.