equations. Show work! 1. \( 2 x+5=13 \) 2. \( 3 x-4=11 \) 11. \( 4 x-6=18 \) 3. \( 4 x+7=23 \) 12. \( 0.25 x+5=\varepsilon \) 4. \( 5 x-3=17 \) 5. \( 3 x+2=11 \) 6. \( 7 x-9=20 \) 7. \( \frac{1}{2} x+6=10 \) 8. \( 2 x-5=13 \) 9. \( 0.5 x+4=9 \) 10. \( 3 x+1=10 \)

Let's solve the equations one by one! 1. \( 2x + 5 = 13 \) Subtract 5 from both sides: \( 2x = 8 \) Divide by 2: \( x = 4 \) 2. \( 3x - 4 = 11 \) Add 4 to both sides: \( 3x = 15 \) Divide by 3: \( x = 5 \) 11. \( 4x - 6 = 18 \) Add 6 to both sides: \( 4x = 24 \) Divide by 4: \( x = 6 \) 3. \( 4x + 7 = 23 \) Subtract 7 from both sides: \( 4x = 16 \) Divide by 4: \( x = 4 \) 12. \( 0.25x + 5 = \varepsilon \) Subtract 5 from both sides: \( 0.25x = \varepsilon - 5 \) Multiply by 4: \( x = 4\varepsilon - 20 \) 4. \( 5x - 3 = 17 \) Add 3 to both sides: \( 5x = 20 \) Divide by 5: \( x = 4 \) 5. \( 3x + 2 = 11 \) Subtract 2 from both sides: \( 3x = 9 \) Divide by 3: \( x = 3 \) 6. \( 7x - 9 = 20 \) Add 9 to both sides: \( 7x = 29 \) Divide by 7: \( x \approx 4.14 \) 7. \( \frac{1}{2}x + 6 = 10 \) Subtract 6 from both sides: \( \frac{1}{2}x = 4 \) Multiply by 2: \( x = 8 \) 8. \( 2x - 5 = 13 \) Add 5 to both sides: \( 2x = 18 \) Divide by 2: \( x = 9 \) 9. \( 0.5x + 4 = 9 \) Subtract 4 from both sides: \( 0.5x = 5 \) Multiply by 2: \( x = 10 \) 10. \( 3x + 1 = 10 \) Subtract 1 from both sides: \( 3x = 9 \) Divide by 3: \( x = 3 \) And there you have it! All equations solved. 🌟