c. Resolver las siguientes ecuaciones. \( \begin{array}{ll}\text { 1. } 2(x+2)=8 & \text { 2. } 3(4-x)=12 \\ 3.2(x+2)=4 x & \text { 4. } 2(x+5)=3 x \\ \text { 5. } 3(2-x)=4+x & \text { 6. } 3(3-2 x)=-4-2 x \\ \text { 7. } 2(3-x)=5 x-6 & \text { 8. } 5(2-2 x)=6-5 x \\ \text { 9. }-3(x-2)=6 x-3+x & \text { 10. } 1+2(x+2)=-3(1+x)\end{array} \)

Solve the equation by following steps: - step0: Solve for \(x\): \(3\left(4-x\right)=12\) - step1: Divide both sides: \(\frac{3\left(4-x\right)}{3}=\frac{12}{3}\) - step2: Divide the numbers: \(4-x=4\) - step3: Move the constant to the right side: \(-x=4-4\) - step4: Subtract the numbers: \(-x=0\) - step5: Change the signs: \(x=0\) Solve the equation \( 3(2-x)=4+x \). Solve the equation by following steps: - step0: Solve for \(x\): \(3\left(2-x\right)=4+x\) - step1: Expand the expression: \(6-3x=4+x\) - step2: Move the expression to the left side: \(-3x-x=4-6\) - step3: Add and subtract: \(-4x=4-6\) - step4: Add and subtract: \(-4x=-2\) - step5: Change the signs: \(4x=2\) - step6: Divide both sides: \(\frac{4x}{4}=\frac{2}{4}\) - step7: Divide the numbers: \(x=\frac{1}{2}\) Solve the equation \( 2(3-x)=5 x-6 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2\left(3-x\right)=5x-6\) - step1: Expand the expression: \(6-2x=5x-6\) - step2: Move the expression to the left side: \(-2x-5x=-6-6\) - step3: Add and subtract: \(-7x=-6-6\) - step4: Add and subtract: \(-7x=-12\) - step5: Change the signs: \(7x=12\) - step6: Divide both sides: \(\frac{7x}{7}=\frac{12}{7}\) - step7: Divide the numbers: \(x=\frac{12}{7}\) Solve the equation \( 1+2(x+2)=-3(1+x) \). Solve the equation by following steps: - step0: Solve for \(x\): \(1+2\left(x+2\right)=-3\left(1+x\right)\) - step1: Calculate: \(5+2x=-3\left(1+x\right)\) - step2: Calculate: \(5+2x=-3-3x\) - step3: Move the expression to the left side: \(5+2x-\left(-3-3x\right)=0\) - step4: Calculate: \(8+5x=0\) - step5: Move the constant to the right side: \(5x=0-8\) - step6: Remove 0: \(5x=-8\) - step7: Divide both sides: \(\frac{5x}{5}=\frac{-8}{5}\) - step8: Divide the numbers: \(x=-\frac{8}{5}\) Solve the equation \( 3(3-2 x)=-4-2 x \). Solve the equation by following steps: - step0: Solve for \(x\): \(3\left(3-2x\right)=-4-2x\) - step1: Expand the expression: \(9-6x=-4-2x\) - step2: Move the expression to the left side: \(-6x+2x=-4-9\) - step3: Add and subtract: \(-4x=-4-9\) - step4: Add and subtract: \(-4x=-13\) - step5: Change the signs: \(4x=13\) - step6: Divide both sides: \(\frac{4x}{4}=\frac{13}{4}\) - step7: Divide the numbers: \(x=\frac{13}{4}\) Solve the equation \( 2(x+2)=8 \). Solve the equation by following steps: - step0: Solve for \(x\): \(2\left(x+2\right)=8\) - step1: Divide both sides: \(\frac{2\left(x+2\right)}{2}=\frac{8}{2}\) - step2: Divide the numbers: \(x+2=4\) - step3: Move the constant to the right side: \(x=4-2\) - step4: Subtract the numbers: \(x=2\) Solve the equation \( 3.2(x+2)=4 x \). Solve the equation by following steps: - step0: Solve for \(x\): \(3.2\left(x+2\right)=4x\) - step1: Expand the expression: \(3.2x+6.4=4x\) - step2: Move the variable to the left side: \(3.2x+6.4-4x=0\) - step3: Subtract the terms: \(-0.8x+6.4=0\) - step4: Move the constant to the right side: \(-0.8x=0-6.4\) - step5: Remove 0: \(-0.8x=-6.4\) - step6: Change the signs: \(0.8x=6.4\) - step7: Divide both sides: \(\frac{0.8x}{0.8}=\frac{6.4}{0.8}\) - step8: Divide the numbers: \(x=8\) Solve the equation \( 2(x+5)=3 x \). Solve the equation by following steps: - step0: Solve for \(x\): \(2\left(x+5\right)=3x\) - step1: Expand the expression: \(2x+10=3x\) - step2: Move the variable to the left side: \(2x+10-3x=0\) - step3: Subtract the terms: \(-x+10=0\) - step4: Move the constant to the right side: \(-x=0-10\) - step5: Remove 0: \(-x=-10\) - step6: Change the signs: \(x=10\) Solve the equation \( 5(2-2 x)=6-5 x \). Solve the equation by following steps: - step0: Solve for \(x\): \(5\left(2-2x\right)=6-5x\) - step1: Expand the expression: \(10-10x=6-5x\) - step2: Move the expression to the left side: \(-10x+5x=6-10\) - step3: Add and subtract: \(-5x=6-10\) - step4: Add and subtract: \(-5x=-4\) - step5: Change the signs: \(5x=4\) - step6: Divide both sides: \(\frac{5x}{5}=\frac{4}{5}\) - step7: Divide the numbers: \(x=\frac{4}{5}\) Solve the equation \( -3(x-2)=6 x-3+x \). Solve the equation by following steps: - step0: Solve for \(x\): \(-3\left(x-2\right)=6x-3+x\) - step1: Add the terms: \(-3\left(x-2\right)=7x-3\) - step2: Expand the expression: \(-3x+6=7x-3\) - step3: Move the expression to the left side: \(-3x-7x=-3-6\) - step4: Add and subtract: \(-10x=-3-6\) - step5: Add and subtract: \(-10x=-9\) - step6: Change the signs: \(10x=9\) - step7: Divide both sides: \(\frac{10x}{10}=\frac{9}{10}\) - step8: Divide the numbers: \(x=\frac{9}{10}\) Aquí están las soluciones para las ecuaciones dadas: 1. **Ecuación:** \( 2(x+2)=8 \) **Solución:** \( x=2 \) 2. **Ecuación:** \( 3(4-x)=12 \) **Solución:** \( x=0 \) 3. **Ecuación:** \( 3.2(x+2)=4 x \) **Solución:** \( x=8 \) 4. **Ecuación:** \( 2(x+5)=3 x \) **Solución:** \( x=10 \) 5. **Ecuación:** \( 3(2-x)=4+x \) **Solución:** \( x=\frac{1}{2} \) o \( x=0.5 \) 6. **Ecuación:** \( 3(3-2 x)=-4-2 x \) **Solución:** \( x=\frac{13}{4} \) o \( x=3.25 \) 7. **Ecuación:** \( 2(3-x)=5 x-6 \) **Solución:** \( x=\frac{12}{7} \) o \( x=1.\dot{7}1428\dot{5} \) 8. **Ecuación:** \( 5(2-2 x)=6-5 x \) **Solución:** \( x=\frac{4}{5} \) o \( x=0.8 \) 9. **Ecuación:** \( -3(x-2)=6 x-3+x \) **Solución:** \( x=\frac{9}{10} \) o \( x=0.9 \) 10. **Ecuación:** \( 1+2(x+2)=-3(1+x) \) **Solución:** \( x=-\frac{8}{5} \) o \( x=-1.6 \) Si necesitas más detalles sobre algún paso en particular, no dudes en preguntar.