\( \begin{array}{r}\text { Solve the following two-step } \\ \text { equations. Show work! }\end{array} \) \( \begin{array}{l}1.2 x+5=13 \\ \text { 2. } 3 x-4=11 \quad 11.4 x-6=18 \\ \text { 3. } 4 x+7=23 \\ \text { 4. } 5 x-3=17 \\ \text { 5. } 3 x+2=11 \\ \text { 6. } 7 x-9=20 \\ \text { 7. } \frac{1}{2} x+6=10 \\ \text { 8. } 2 x-5=13 \\ \text { 9. } 0 \cdot 5 x+4=9 \\ \text { 10. } 3 x+1=10\end{array} \)

Let's solve each of these two-step equations step by step: 1. **\(1.2x + 5 = 13\)** - Subtract 5 from both sides: \(1.2x = 13 - 5\) \(1.2x = 8\) - Divide by 1.2: \(x = \frac{8}{1.2} = \frac{80}{12} = \frac{20}{3} \approx 6.67\) 2. **\(3x - 4 = 11\)** - Add 4 to both sides: \(3x = 11 + 4\) \(3x = 15\) - Divide by 3: \(x = 5\) 3. **\(4x + 7 = 23\)** - Subtract 7 from both sides: \(4x = 23 - 7\) \(4x = 16\) - Divide by 4: \(x = 4\) 4. **\(5x - 3 = 17\)** - Add 3 to both sides: \(5x = 17 + 3\) \(5x = 20\) - Divide by 5: \(x = 4\) 5. **\(3x + 2 = 11\)** - Subtract 2 from both sides: \(3x = 11 - 2\) \(3x = 9\) - Divide by 3: \(x = 3\) 6. **\(7x - 9 = 20\)** - Add 9 to both sides: \(7x = 20 + 9\) \(7x = 29\) - Divide by 7: \(x = \frac{29}{7} \approx 4.14\) 7. **\(\frac{1}{2}x + 6 = 10\)** - Subtract 6 from both sides: \(\frac{1}{2}x = 10 - 6\) \(\frac{1}{2}x = 4\) - Multiply by 2: \(x = 8\) 8. **\(2x - 5 = 13\)** - Add 5 to both sides: \(2x = 13 + 5\) \(2x = 18\) - Divide by 2: \(x = 9\) 9. **\(0 \cdot 5x + 4 = 9\)** (Here, \(0 \cdot 5x = 0\), so it simplifies to \(4 = 9\), which is not possible.) - This means there is no solution for this equation as it's inconsistent. 10. **\(3x + 1 = 10\)** - Subtract 1 from both sides: \(3x = 10 - 1\) \(3x = 9\) - Divide by 3: \(x = 3\) Here's a summary of the solutions: 1: \( \frac{20}{3} \) or approximately 6.67 2: 5 3: 4 4: 4 5: 3 6: \( \frac{29}{7} \) or approximately 4.14 7: 8 8: 9 9: No solution 10: 3