Equations Expanding Brackets \( 13(a-6)=8 \) \( 2 \quad 8(a-2)=20 \) \( 3 \quad 5(a+7)=45 \) \( 4 \quad 9(a-1)=18 \) \( 5 \quad 6(2 a+3)=30 a \) \( 6 \quad 7(a-3)=2(a+7) \) \( 76(b+2)=4(b+5) \) \( 8 \quad 5(2 b-3)=7(b+3) \) \( 9 \quad 3(a+6)=a+22 \) \( 107 m-4=3(m+4) \) \( 114(5-b)=b \) \( 126(n+2)=4 n+15 \) \( 132(3 a-7)+4=3(a+2)+2 \) \( 145 a-(1-2 a)=5-3(1+a) \) \( 154(b-1)-3(b-2)=4-5 b \)

Solve the equation by following steps: - step0: Solve for \(a\): \(9\left(a-1\right)=18\) - step1: Divide both sides: \(\frac{9\left(a-1\right)}{9}=\frac{18}{9}\) - step2: Divide the numbers: \(a-1=2\) - step3: Move the constant to the right side: \(a=2+1\) - step4: Add the numbers: \(a=3\) Solve the equation \( 5(a+7)=45 \). Solve the equation by following steps: - step0: Solve for \(a\): \(5\left(a+7\right)=45\) - step1: Divide both sides: \(\frac{5\left(a+7\right)}{5}=\frac{45}{5}\) - step2: Divide the numbers: \(a+7=9\) - step3: Move the constant to the right side: \(a=9-7\) - step4: Subtract the numbers: \(a=2\) Solve the equation \( 13(a-6)=8 \). Solve the equation by following steps: - step0: Solve for \(a\): \(13\left(a-6\right)=8\) - step1: Divide both sides: \(\frac{13\left(a-6\right)}{13}=\frac{8}{13}\) - step2: Divide the numbers: \(a-6=\frac{8}{13}\) - step3: Move the constant to the right side: \(a=\frac{8}{13}+6\) - step4: Add the numbers: \(a=\frac{86}{13}\) Solve the equation \( 126(n+2)=4 n+15 \). Solve the equation by following steps: - step0: Solve for \(n\): \(126\left(n+2\right)=4n+15\) - step1: Expand the expression: \(126n+252=4n+15\) - step2: Move the expression to the left side: \(126n-4n=15-252\) - step3: Add and subtract: \(122n=15-252\) - step4: Add and subtract: \(122n=-237\) - step5: Divide both sides: \(\frac{122n}{122}=\frac{-237}{122}\) - step6: Divide the numbers: \(n=-\frac{237}{122}\) Solve the equation \( 107 m-4=3(m+4) \). Solve the equation by following steps: - step0: Solve for \(m\): \(107m-4=3\left(m+4\right)\) - step1: Expand the expression: \(107m-4=3m+12\) - step2: Move the expression to the left side: \(107m-3m=12+4\) - step3: Add and subtract: \(104m=12+4\) - step4: Add and subtract: \(104m=16\) - step5: Divide both sides: \(\frac{104m}{104}=\frac{16}{104}\) - step6: Divide the numbers: \(m=\frac{2}{13}\) Solve the equation \( 7(a-3)=2(a+7) \). Solve the equation by following steps: - step0: Solve for \(a\): \(7\left(a-3\right)=2\left(a+7\right)\) - step1: Calculate: \(7a-21=2\left(a+7\right)\) - step2: Calculate: \(7a-21=2a+14\) - step3: Move the expression to the left side: \(7a-21-\left(2a+14\right)=0\) - step4: Calculate: \(5a-35=0\) - step5: Move the constant to the right side: \(5a=0+35\) - step6: Remove 0: \(5a=35\) - step7: Divide both sides: \(\frac{5a}{5}=\frac{35}{5}\) - step8: Divide the numbers: \(a=7\) Solve the equation \( 76(b+2)=4(b+5) \). Solve the equation by following steps: - step0: Solve for \(b\): \(76\left(b+2\right)=4\left(b+5\right)\) - step1: Calculate: \(76b+152=4\left(b+5\right)\) - step2: Calculate: \(76b+152=4b+20\) - step3: Move the expression to the left side: \(76b+152-\left(4b+20\right)=0\) - step4: Calculate: \(72b+132=0\) - step5: Move the constant to the right side: \(72b=0-132\) - step6: Remove 0: \(72b=-132\) - step7: Divide both sides: \(\frac{72b}{72}=\frac{-132}{72}\) - step8: Divide the numbers: \(b=-\frac{11}{6}\) Solve the equation \( 5(2 b-3)=7(b+3) \). Solve the equation by following steps: - step0: Solve for \(b\): \(5\left(2b-3\right)=7\left(b+3\right)\) - step1: Calculate: \(10b-15=7\left(b+3\right)\) - step2: Calculate: \(10b-15=7b+21\) - step3: Move the expression to the left side: \(10b-15-\left(7b+21\right)=0\) - step4: Calculate: \(3b-36=0\) - step5: Move the constant to the right side: \(3b=0+36\) - step6: Remove 0: \(3b=36\) - step7: Divide both sides: \(\frac{3b}{3}=\frac{36}{3}\) - step8: Divide the numbers: \(b=12\) Solve the equation \( 8(a-2)=20 \). Solve the equation by following steps: - step0: Solve for \(a\): \(8\left(a-2\right)=20\) - step1: Divide both sides: \(\frac{8\left(a-2\right)}{8}=\frac{20}{8}\) - step2: Divide the numbers: \(a-2=\frac{5}{2}\) - step3: Move the constant to the right side: \(a=\frac{5}{2}+2\) - step4: Add the numbers: \(a=\frac{9}{2}\) Solve the equation \( 6(2 a+3)=30 a \). Solve the equation by following steps: - step0: Solve for \(a\): \(6\left(2a+3\right)=30a\) - step1: Expand the expression: \(12a+18=30a\) - step2: Move the variable to the left side: \(12a+18-30a=0\) - step3: Subtract the terms: \(-18a+18=0\) - step4: Move the constant to the right side: \(-18a=0-18\) - step5: Remove 0: \(-18a=-18\) - step6: Change the signs: \(18a=18\) - step7: Divide both sides: \(\frac{18a}{18}=\frac{18}{18}\) - step8: Divide the numbers: \(a=1\) Solve the equation \( 114(5-b)=b \). Solve the equation by following steps: - step0: Solve for \(b\): \(114\left(5-b\right)=b\) - step1: Expand the expression: \(570-114b=b\) - step2: Move the variable to the left side: \(570-114b-b=0\) - step3: Subtract the terms: \(570-115b=0\) - step4: Move the constant to the right side: \(-115b=0-570\) - step5: Remove 0: \(-115b=-570\) - step6: Change the signs: \(115b=570\) - step7: Divide both sides: \(\frac{115b}{115}=\frac{570}{115}\) - step8: Divide the numbers: \(b=\frac{114}{23}\) Solve the equation \( 3(a+6)=a+22 \). Solve the equation by following steps: - step0: Solve for \(a\): \(3\left(a+6\right)=a+22\) - step1: Expand the expression: \(3a+18=a+22\) - step2: Move the expression to the left side: \(3a-a=22-18\) - step3: Add and subtract: \(2a=22-18\) - step4: Add and subtract: \(2a=4\) - step5: Divide both sides: \(\frac{2a}{2}=\frac{4}{2}\) - step6: Divide the numbers: \(a=2\) Solve the equation \( 145 a-(1-2 a)=5-3(1+a) \). Solve the equation by following steps: - step0: Solve for \(a\): \(145a-\left(1-2a\right)=5-3\left(1+a\right)\) - step1: Subtract the terms: \(147a-1=5-3\left(1+a\right)\) - step2: Move the expression to the left side: \(147a-1-\left(5-3\left(1+a\right)\right)=0\) - step3: Subtract the terms: \(147a-6+3\left(1+a\right)=0\) - step4: Calculate: \(150a-3=0\) - step5: Move the constant to the right side: \(150a=0+3\) - step6: Remove 0: \(150a=3\) - step7: Divide both sides: \(\frac{150a}{150}=\frac{3}{150}\) - step8: Divide the numbers: \(a=\frac{1}{50}\) Solve the equation \( 132(3 a-7)+4=3(a+2)+2 \). Solve the equation by following steps: - step0: Solve for \(a\): \(132\left(3a-7\right)+4=3\left(a+2\right)+2\) - step1: Move the expression to the left side: \(132\left(3a-7\right)+4-\left(3\left(a+2\right)+2\right)=0\) - step2: Calculate: \(132\left(3a-7\right)+2-3\left(a+2\right)=0\) - step3: Calculate: \(393a-928=0\) - step4: Move the constant to the right side: \(393a=0+928\) - step5: Remove 0: \(393a=928\) - step6: Divide both sides: \(\frac{393a}{393}=\frac{928}{393}\) - step7: Divide the numbers: \(a=\frac{928}{393}\) Solve the equation \( 154(b-1)-3(b-2)=4-5 b \). Solve the equation by following steps: - step0: Solve for \(b\): \(154\left(b-1\right)-3\left(b-2\right)=4-5b\) - step1: Move the expression to the left side: \(154\left(b-1\right)-3\left(b-2\right)-\left(4-5b\right)=0\) - step2: Remove the parentheses: \(154\left(b-1\right)-3\left(b-2\right)-4+5b=0\) - step3: Calculate: \(156b-152=0\) - step4: Move the constant to the right side: \(156b=0+152\) - step5: Remove 0: \(156b=152\) - step6: Divide both sides: \(\frac{156b}{156}=\frac{152}{156}\) - step7: Divide the numbers: \(b=\frac{38}{39}\) Here are the solutions for the equations after expanding the brackets: 1. **Equation:** \( 13(a-6)=8 \) **Solution:** \[ a = \frac{86}{13} \quad \text{or} \quad a \approx 6.615384615 \] 2. **Equation:** \( 8(a-2)=20 \) **Solution:** \[ a = \frac{9}{2} \quad \text{or} \quad a = 4.5 \] 3. **Equation:** \( 5(a+7)=45 \) **Solution:** \[ a = 2 \] 4. **Equation:** \( 9(a-1)=18 \) **Solution:** \[ a = 3 \] 5. **Equation:** \( 6(2 a+3)=30 a \) **Solution:** \[ a = 1 \] 6. **Equation:** \( 7(a-3)=2(a+7) \) **Solution:** \[ a = 7 \] 7. **Equation:** \( 76(b+2)=4(b+5) \) **Solution:** \[ b = -\frac{11}{6} \quad \text{or} \quad b \approx -1.8333 \] 8. **Equation:** \( 5(2 b-3)=7(b+3) \) **Solution:** \[ b = 12 \] 9. **Equation:** \( 3(a+6)=a+22 \) **Solution:** \[ a = 2 \] 10. **Equation:** \( 107 m-4=3(m+4) \) **Solution:** \[ m = \frac{2}{13} \quad \text{or} \quad m \approx 0.1538461538 \] 11. **Equation:** \( 114(5-b)=b \) **Solution:** \[ b = \frac{114}{23} \quad \text{or} \quad b \approx 4.9565217391 \] 12. **Equation:** \( 126(n+2)=4 n+15 \) **Solution:** \[ n = -\frac{237}{122} \quad \text{or} \quad n \approx -1.94344262295 \] 13. **Equation:** \( 132(3 a-7)+4=3(a+2)+2 \) **Solution:** \[ a = \frac{928}{393} \quad \text{or} \quad a \approx 2.36 \] 14. **Equation:** \( 145 a-(1-2 a)=5-3(1+a) \) **Solution:** \[ a = \frac{1}{50} \quad \text{or} \quad a = 0.02 \] 15. **Equation:** \( 154(b-1)-3(b-2)=4-5 b \) **Solution:** \[ b = \frac{38}{39} \quad \text{or} \quad b \approx 0.97435897436 \] If you need further assistance or explanations for any specific equation, feel free to ask!