equations. 1. $$ 2 x+5=13 $$ 2. $$ 3 x-4=11 $$ 3. $$ 4 x+7=23 $$ 4. $$ 5 x-3=17 $$ 5. $$ 3 x+2=11 $$ 6. $$ 7 x-9=20 $$ 7. $$ \frac{1}{2} x+6=10 $$ 1. $$ 2 x-5=13 $$

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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 both sides by 3:  
  $$
  x = \frac{15}{3} = 5
  $$

---

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

---

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

---

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

---

**6. Solve $$7x - 9 = 20$$**
  
- Add 9 to both sides:  
  $$
  7x = 20 + 9 = 29
  $$
- Divide both sides 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 both sides by 2:  
  $$
  x = \frac{18}{2} = 9
  $$
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. $$ x = 9 $$

equations. 1. \( 2 x+5=13 \) 2. \( 3 x-4=11 \) 3. \( 4 x+7=23 \) 4. \( 5 x-3=17 \) 5. \( 3 x+2=11 \) 6. \( 7 x-9=20 \) 7. \( \frac{1}{2} x+6=10 \) 1. \( 2 x-5=13 \)

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