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. \( 2 x-5=13 \)

**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: \[ x = \frac{18}{2} = 9 \]