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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Let’s tackle each equation step by step! 1. **Equation**: \( 2x + 5 = 13 \) **Step 1**: Subtract 5 from both sides: \( 2x = 13 - 5 \) \( 2x = 8 \) **Step 2**: Divide both sides by 2: \( x = \frac{8}{2} \) \( x = 4 \) 2. **Equation**: \( 3x - 4 = 11 \) **Step 1**: Add 4 to both sides: \( 3x = 11 + 4 \) \( 3x = 15 \) **Step 2**: Divide both sides by 3: \( x = \frac{15}{3} \) \( x = 5 \) 3. **Equation**: \( 11.4x - 6 = 18 \) **Step 1**: Add 6 to both sides: \( 11.4x = 18 + 6 \) \( 11.4x = 24 \) **Step 2**: Divide both sides by 11.4: \( x = \frac{24}{11.4} \) \( x \approx 2.1053 \) (rounded to four decimal places) 4. **Equation**: \( 4x + 7 = 23 \) **Step 1**: Subtract 7 from both sides: \( 4x = 23 - 7 \) \( 4x = 16 \) **Step 2**: Divide both sides by 4: \( x = \frac{16}{4} \) \( x = 4 \) 5. **Equation**: \( 0.25x + 5 = \varepsilon \) **Step 1**: Subtract 5 from both sides: \( 0.25x = \varepsilon - 5 \) **Step 2**: Divide both sides by 0.25: \( x = \frac{\varepsilon - 5}{0.25} \) \( x = 4(\varepsilon - 5) \) 6. **Equation**: \( 5x - 3 = 17 \) **Step 1**: Add 3 to both sides: \( 5x = 17 + 3 \) \( 5x = 20 \) **Step 2**: Divide both sides by 5: \( x = \frac{20}{5} \) \( x = 4 \) 7. **Equation**: \( 3x + 2 = 11 \) **Step 1**: Subtract 2 from both sides: \( 3x = 11 - 2 \) \( 3x = 9 \) **Step 2**: Divide both sides by 3: \( x = \frac{9}{3} \) \( x = 3 \) 8. **Equation**: \( 7x - 9 = 20 \) **Step 1**: Add 9 to both sides: \( 7x = 20 + 9 \) \( 7x = 29 \) **Step 2**: Divide both sides by 7: \( x = \frac{29}{7} \) \( x \approx 4.1429 \) 9. **Equation**: \( \frac{1}{2}x + 6 = 10 \) **Step 1**: Subtract 6 from both sides: \( \frac{1}{2}x = 10 - 6 \) \( \frac{1}{2}x = 4 \) **Step 2**: Multiply both sides by 2: \( x = 4 \times 2 \) \( x = 8 \) 10. **Equation**: \( 2x - 5 = 13 \) **Step 1**: Add 5 to both sides: \( 2x = 13 + 5 \) \( 2x = 18 \) **Step 2**: Divide both sides by 2: