Solve these inequalities on paper. Type in your answer as \( x< \) ? or \( x> \) ? \[ \begin{array}{l} -x<-2 \\ -x>3 \\ 7-x>0 \\ 15-x<10 \\ -2 x>4 \\ 18-3 x \square \\ -10-7 x>11 \end{array} \] Sean is thinking of a number. When I double it and take the result away from 23 the answer is less than 13. What number could Sean be thinking of? Type in your answer as \( x< \) ? or \( x> \) ? \( \square \) [2] [7]

To solve the inequalities, let's tackle each one step-by-step. 1. For \( -x < -2 \): Multiply by -1 (flip the inequality) gives \( x > 2 \). 2. For \( -x > 3 \): Multiply by -1 (flip the inequality) gives \( x < -3 \). 3. For \( 7 - x > 0 \): Rearranging gives \( -x > -7 \) which simplifies to \( x < 7 \). 4. For \( 15 - x < 10 \): Rearranging gives \( -x < -5 \) which simplifies to \( x > 5 \). 5. For \( -2x > 4 \): Divide by -2 (flip the inequality) gives \( x < -2 \). 6. For \( 18 - 3x \square \): If we apply a common greater than or less than (let's use >), we can say \( x < 6 \). 7. For \( -10 - 7x > 11 \): Rearranging gives \( -7x > 21 \), dividing by -7 (flipping the inequality) gives \( x < -3 \). Now, parsing the inequalities, we have: - \( x > 2 \) - \( x < -3 \) - \( x < 7 \) - \( x > 5 \) - \( x < -2 \) - \( x < 6 \) - \( x < -3 \) Now for Sean's problem, let's break it down: The expression is \( 23 - 2x < 13 \). Rearranging gives \( -2x < -10 \), dividing by -2 gives \( x > 5 \). Consolidating our answers: 1. \( x < -3 \) 2. \( x < -3 \) 3. \( x < 7 \) 4. \( x > 5 \) 5. \( x < -2 \) 6. \( x < 6 \) 7. \( x < -3 \) Sean's number leads us to: \( x > 5 \)