Penelope is playing a number game with her sister June. Penelope is thinking of a number and wants June to guess it. Five more than three times her number is between -4 and 23 . Write a compound inequality tha shows the range of numbers that Penelope might be thinking of. Submit Question Jump to Answer

Let \( x \) represent the number Penelope is thinking of. According to the problem: "Five more than three times her number is between -4 and 23." This can be translated into the following compound inequality: \[ -4 < 3x + 5 < 23 \] To find the range of possible values for \( x \), solve the inequality step by step: 1. **Subtract 5 from all parts of the inequality:** \[ -4 - 5 < 3x < 23 - 5 \] \[ -9 < 3x < 18 \] 2. **Divide all parts of the inequality by 3:** \[ \frac{-9}{3} < x < \frac{18}{3} \] \[ -3 < x < 6 \] **Final Range:** \[ -3 < x < 6 \] So, the range of numbers that Penelope might be thinking of is all real numbers \( x \) such that \( -3 < x < 6 \). **Answer:** All real numbers x with –3 < x < 6. In symbols, the compound inequality is –3 < x < 6.