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. $$ 3 x+1=10 $$

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**1. Solve $$ 2x+5=13 $$:**  
Subtract 5 from both sides:  
$$
2x = 13 - 5 = 8
$$  
Divide both sides by 2:  
$$
x = \frac{8}{2} = 4
$$

**2. Solve $$ 3x-4=11 $$:**  
Add 4 to both sides:  
$$
3x = 11 + 4 = 15
$$  
Divide by 3:  
$$
x = \frac{15}{3} = 5
$$

**(Additional Equation) Solve $$ 11.4x-6=18 $$:**  
Add 6 to both sides:  
$$
11.4x = 18 + 6 = 24
$$  
Divide by 11.4:  
$$
x = \frac{24}{11.4} = \frac{240}{114} = \frac{40}{19}
$$

**3. Solve $$ 4x+7=23 $$:**  
Subtract 7 from both sides:  
$$
4x = 23 - 7 = 16
$$  
Divide by 4:  
$$
x = \frac{16}{4} = 4
$$

**(Additional Equation) Solve $$ 0.25x+5=\varepsilon $$:**  
Subtract 5 from both sides:  
$$
0.25x = \varepsilon - 5
$$  
Divide by 0.25 (which is equivalent to multiplying by 4):  
$$
x = 4(\varepsilon - 5) = 4\varepsilon - 20
$$

**4. Solve $$ 5x-3=17 $$:**  
Add 3 to both sides:  
$$
5x = 17 + 3 = 20
$$  
Divide by 5:  
$$
x = \frac{20}{5} = 4
$$

**5. Solve $$ 3x+2=11 $$:**  
Subtract 2 from both sides:  
$$
3x = 11 - 2 = 9
$$  
Divide by 3:  
$$
x = \frac{9}{3} = 3
$$

**6. Solve $$ 7x-9=20 $$:**  
Add 9 to both sides:  
$$
7x = 20 + 9 = 29
$$  
Divide by 7:  
$$
x = \frac{29}{7}
$$

**7. Solve $$ \frac{1}{2}x+6=10 $$:**  
Subtract 6 from both sides:  
$$
\frac{1}{2}x = 10 - 6 = 4
$$  
Multiply both sides by 2:  
$$
x = 4 \times 2 = 8
$$

**8. Solve $$ 2x-5=13 $$:**  
Add 5 to both sides:  
$$
2x = 13 + 5 = 18
$$  
Divide by 2:  
$$
x = \frac{18}{2} = 9
$$

**9. Solve $$ 0.5x+4=9 $$:**  
Subtract 4 from both sides:  
$$
0.5x = 9 - 4 = 5
$$  
Divide by 0.5:  
$$
x = \frac{5}{0.5} = 10
$$

**10. Solve $$ 3x+1=10 $$:**  
Subtract 1 from both sides:  
$$
3x = 10 - 1 = 9
$$  
Divide by 3:  
$$
x = \frac{9}{3} = 3
$$
Here are the solutions to the equations: 1. $$ x = 4 $$ 2. $$ x = 5 $$ 3. $$ x = 4 $$ 4. $$ x = 4 $$ 5. $$ x = 3 $$ 6. $$ x = \frac{29}{7} $$ 7. $$ x = 8 $$ 8. $$ x = 9 $$ 9. $$ x = 10 $$ 10. $$ x = 3 $$

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. \( 3 x+1=10 \)

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