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

Question

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

UpStudy AI · Accepted Answer

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.
Aquí están las soluciones para las ecuaciones: 1. $$ x = 2 $$ 2. $$ x = 0 $$ 3. $$ x = 8 $$ 4. $$ x = 10 $$ 5. $$ x = 0.5 $$ 6. $$ x = 3.25 $$ 7. $$ x \approx 1.714 $$ 8. $$ x = 0.8 $$ 9. $$ x = 0.9 $$ 10. $$ x = -1.6 $$

c. Resolver las siguientes ecuaciones.

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