To solve the inequality 25 < 12x < 65 < 32x, we will break it down into two parts: the first part is 25 < 12x, and the second part is 65 < 32x.
Step 1: Solve the first inequality (25 < 12x)
- Divide both sides by 12: x > 25/12
- Calculating 25/12 gives us approximately 2.08. Therefore, x > 2.08.
Step 2: Solve the second inequality (65 < 32x)
- Divide both sides by 32: x > 65/32
- Calculating 65/32 gives us approximately 2.03. Therefore, x > 2.03.
Step 3: Combine the solutions
Since we have x > 2.08 and x > 2.03, the constraint that is most limiting is x > 2.08.
This means that the solution can be represented on a number line starting at approximately 2.08 and extending to the right. If we were to visualize this on a number line, you would have an open circle at 2.08 indicating that 2.08 is not included, and a line extending to the right to represent all numbers greater than 2.08.