phrase I. The difference between three times \( x \) and fifteen is greater than or equal to five 2. Five more than sixteen times \( x \) is less than or equal to six 3. Three more than two times \( x \) is less than seven \( \square \) 4. Five less than four times \( x \) is less than or equal to sixteen 5. Six times the sum of \( x \) and twelve is less than fourteen 6. The difference between fifteen and two times \( x \) is greater than five 7. The difference between eleven and four times \( x \) is greater than or equal to three 8. The sum of negative three times \( x \) and five is less than or equal to negative four 9. Fourteen less than five times \( x \) is at most eleven \( \qquad \) 10. Twice the sum of nine and \( x \) is greater than twenty II. Ten less than three times \( x \) is greater than eleven 12. Thirteen plus five times \( x \) is no more than thirty 13. Thirteen more than three times \( x \) is no more than the opposite of eleven 14. Half of the sum of \( x \) and six is no less than twenty 15. The difference between negative five times \( x \) and eight is greater than twelve. Solve only your inequalities! Look for your answer at the bottom. \[ \begin{array}{ll} N \quad 2 x+3 \leq 7 & E \\ C & 14-5 x \leq 11 \\ \text { C } 15-2 x>5 & \text { R } \\ F(9+x)>20 \\ E \quad 1 / 2 x+6 x \leq 30 & \text { D } \end{array} 6(x+12)<141 \] \[ \text { L } 5 x-14 \leq 11 \quad H \quad-3 x-5<-4 \] \[ \text { U } 3 x-15 \geq 5 \quad \text { A } 1 / 2(x+6) \geq 20 \] \[ E \quad 6(x-12)>14 \backslash \text { H } \quad 11-4 x \geq 3 \] \[ 3 x-10>11 \quad 0 \quad-5 x-8>12 \] \[ \vee 16 x+5<6 \quad \& \quad 3 x+13 \leq-11 \] \[ \text { Y } 4 x-5 \geq 16 \quad \text { \& } 16 x+5 \leq 6 \]

Let's solve the inequalities step by step. ### Inequalities to Solve 1. \( 2x + 3 \leq 7 \) 2. \( 14 - 5x \leq 11 \) 3. \( 15 - 2x > 5 \) 4. \( 6(x + 12) < 141 \) 5. \( 5x - 14 \leq 11 \) 6. \( -3x - 5 < -4 \) 7. \( 3x - 15 \geq 5 \) 8. \( \frac{1}{2}(x + 6) \geq 20 \) 9. \( 6(x - 12) > 14 \) 10. \( 11 - 4x \geq 3 \) 11. \( 3x - 10 > 11 \) 12. \( -5x - 8 > 12 \) 13. \( 16x + 5 < 6 \) 14. \( 3x + 13 \leq -11 \) 15. \( 4x - 5 \geq 16 \) ### Step-by-Step Solutions 1. **Solve \( 2x + 3 \leq 7 \)**: \[ 2x \leq 7 - 3 \\ 2x \leq 4 \\ x \leq 2 \] 2. **Solve \( 14 - 5x \leq 11 \)**: \[ -5x \leq 11 - 14 \\ -5x \leq -3 \\ x \geq \frac{3}{5} \] 3. **Solve \( 15 - 2x > 5 \)**: \[ -2x > 5 - 15 \\ -2x > -10 \\ x < 5 \] 4. **Solve \( 6(x + 12) < 141 \)**: \[ x + 12 < \frac{141}{6} \\ x + 12 < 23.5 \\ x < 23.5 - 12 \\ x < 11.5 \] 5. **Solve \( 5x - 14 \leq 11 \)**: \[ 5x \leq 11 + 14 \\ 5x \leq 25 \\ x \leq 5 \] 6. **Solve \( -3x - 5 < -4 \)**: \[ -3x < -4 + 5 \\ -3x < 1 \\ x > -\frac{1}{3} \] 7. **Solve \( 3x - 15 \geq 5 \)**: \[ 3x \geq 5 + 15 \\ 3x \geq 20 \\ x \geq \frac{20}{3} \] 8. **Solve \( \frac{1}{2}(x + 6) \geq 20 \)**: \[ x + 6 \geq 40 \\ x \geq 40 - 6 \\ x \geq 34 \] 9. **Solve \( 6(x - 12) > 14 \)**: \[ x - 12 > \frac{14}{6} \\ x - 12 > \frac{7}{3} \\ x > 12 + \frac{7}{3} \\ x > \frac{36}{3} + \frac{7}{3} \\ x > \frac{43}{3} \] 10. **Solve \( 11 - 4x \geq 3 \)**: \[ -4x \geq 3 - 11 \\ -4x \geq -8 \\ x \leq 2 \] 11. **Solve \( 3x - 10 > 11 \)**: \[ 3x > 11 + 10 \\ 3x > 21 \\ x > 7 \] 12. **Solve \( -5x - 8 > 12 \)**: \[ -5x > 12 + 8 \\ -5x > 20 \\ x < -4 \] 13. **Solve \( 16x + 5 < 6 \)**: \[ 16x < 6 - 5 \\ 16x < 1 \\ x < \frac{1}{16} \] 14. **Solve \( 3x + 13 \leq -11 \)**: \[ 3x \leq -11 - 13 \\ 3x \leq -24 \\ x \leq -8 \] 15. **Solve \( 4x - 5 \geq 16 \)**: \[ 4x \geq 16 + 5 \\ 4x \geq 21 \\ x \geq \frac{21}{4} \] ### Summary of Solutions 1. \( x \leq 2 \) 2. \( x \geq \frac{3}{5} \) 3. \( x < 5 \) 4. \( x < 11.5 \) 5. \( x \leq 5 \) 6. \( x > -\frac{1}{3} \) 7. \( x \geq \frac{20}{3} \) 8. \( x \geq 34 \) 9. \( x > \frac{43}{3} \) 10. \( x \leq 2 \) 11. \( x > 7 \) 12. \( x < -4 \) 13. \( x < \frac{1}{16} \) 14. \( x \leq -8 \) 15. \( x \geq \frac{21}{4} \) These inequalities can be further analyzed for intersections or unions based on specific requirements.