Solve the following two-step 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. \( 3 x+1=10 \)

Sure! Let's solve these two-step equations step by step. 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: \( x = 5 \) 3. \( 4x - 6 = 18 \) - Add 6 to both sides: \( 4x = 24 \) - Divide by 4: \( x = 6 \) 4. \( 4x + 7 = 23 \) - Subtract 7 from both sides: \( 4x = 16 \) - Divide by 4: \( x = 4 \) 5. \( 0.25x + 5 = \varepsilon \) - Subtract 5 from both sides: \( 0.25x = \varepsilon - 5 \) - Multiply by 4 to clear the fraction: \( x = 4(\varepsilon - 5) \) 6. \( 5x - 3 = 17 \) - Add 3 to both sides: \( 5x = 20 \) - Divide by 5: \( x = 4 \) 7. \( 3x + 2 = 11 \) - Subtract 2 from both sides: \( 3x = 9 \) - Divide by 3: \( x = 3 \) 8. \( 7x - 9 = 20 \) - Add 9 to both sides: \( 7x = 29 \) - Divide by 7: \( x = \frac{29}{7} \) or approximately \( 4.14 \) 9. \( \frac{1}{2}x + 6 = 10 \) - Subtract 6 from both sides: \( \frac{1}{2}x = 4 \) - Multiply by 2: \( x = 8 \) 10. \( 2x - 5 = 13 \) - Add 5 to both sides: \( 2x = 18 \) - Divide by 2: \( x = 9 \) 11. \( 0.5x + 4 = 9 \) - Subtract 4 from both sides: \( 0.5x = 5 \) - Multiply by 2: \( x = 10 \) 12. \( 3x + 1 = 10 \) - Subtract 1 from both sides: \( 3x = 9 \) - Divide by 3: \( x = 3 \) And voila! You’ve got your solutions for those two-step equations!