21. Calcula la letra $$ \frac{2 x}{3}=15 $$ $$ 22-\frac{6 x+1}{3}=5 $$ $$ 23-\frac{6}{x}=3 $$ $$ 24-\frac{12}{x}=4 $$

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21. Calcula la letra $$ \frac{2 x}{3}=15 $$ $$ 22-\frac{6 x+1}{3}=5 $$ $$ 23-\frac{6}{x}=3 $$ $$ 24-\frac{12}{x}=4 $$

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2x}{3}=15$$
- step1: Cross multiply:
  $$2x=3\times 15$$
- step2: Simplify the equation:
  $$2x=45$$
- step3: Divide both sides:
  $$\frac{2x}{2}=\frac{45}{2}$$
- step4: Divide the numbers:
  $$x=\frac{45}{2}$$
Solve the equation $$ 23-\frac{6}{x}=3 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$23-\frac{6}{x}=3$$
- step1: Find the domain:
  $$23-\frac{6}{x}=3,x\neq 0$$
- step2: Move the constant to the right side:
  $$-\frac{6}{x}=3-23$$
- step3: Subtract the numbers:
  $$-\frac{6}{x}=-20$$
- step4: Rewrite the expression:
  $$\frac{-6}{x}=-20$$
- step5: Cross multiply:
  $$-6=x\left(-20\right)$$
- step6: Simplify the equation:
  $$-6=-20x$$
- step7: Rewrite the expression:
  $$-2\times 3=-2\times 10x$$
- step8: Evaluate:
  $$3=10x$$
- step9: Swap the sides:
  $$10x=3$$
- step10: Divide both sides:
  $$\frac{10x}{10}=\frac{3}{10}$$
- step11: Divide the numbers:
  $$x=\frac{3}{10}$$
- step12: Check if the solution is in the defined range:
  $$x=\frac{3}{10},x\neq 0$$
- step13: Find the intersection:
  $$x=\frac{3}{10}$$
Solve the equation $$ 24-\frac{12}{x}=4 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$24-\frac{12}{x}=4$$
- step1: Find the domain:
  $$24-\frac{12}{x}=4,x\neq 0$$
- step2: Move the constant to the right side:
  $$-\frac{12}{x}=4-24$$
- step3: Subtract the numbers:
  $$-\frac{12}{x}=-20$$
- step4: Rewrite the expression:
  $$\frac{-12}{x}=-20$$
- step5: Cross multiply:
  $$-12=x\left(-20\right)$$
- step6: Simplify the equation:
  $$-12=-20x$$
- step7: Rewrite the expression:
  $$-4\times 3=-4\times 5x$$
- step8: Evaluate:
  $$3=5x$$
- step9: Swap the sides:
  $$5x=3$$
- step10: Divide both sides:
  $$\frac{5x}{5}=\frac{3}{5}$$
- step11: Divide the numbers:
  $$x=\frac{3}{5}$$
- step12: Check if the solution is in the defined range:
  $$x=\frac{3}{5},x\neq 0$$
- step13: Find the intersection:
  $$x=\frac{3}{5}$$
Solve the equation $$ 22-\frac{6 x+1}{3}=5 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$22-\frac{6x+1}{3}=5$$
- step1: Multiply both sides of the equation by LCD:
  $$\left(22-\frac{6x+1}{3}\right)\times 3=5\times 3$$
- step2: Simplify the equation:
  $$65-6x=15$$
- step3: Move the constant to the right side:
  $$-6x=15-65$$
- step4: Subtract the numbers:
  $$-6x=-50$$
- step5: Change the signs:
  $$6x=50$$
- step6: Divide both sides:
  $$\frac{6x}{6}=\frac{50}{6}$$
- step7: Divide the numbers:
  $$x=\frac{25}{3}$$
Aquí están las soluciones para cada una de las ecuaciones:

1. Para la ecuación $$ \frac{2 x}{3} = 15 $$:
   $$
   x = \frac{45}{2} \quad \text{o} \quad x = 22.5
   $$

2. Para la ecuación $$ 22 - \frac{6 x + 1}{3} = 5 $$:
   $$
   x = \frac{25}{3} \quad \text{o} \quad x = 8.\dot{3}
   $$

3. Para la ecuación $$ 23 - \frac{6}{x} = 3 $$:
   $$
   x = \frac{3}{10} \quad \text{o} \quad x = 0.3
   $$

4. Para la ecuación $$ 24 - \frac{12}{x} = 4 $$:
   $$
   x = \frac{3}{5} \quad \text{o} \quad x = 0.6
   $$

Si necesitas más ayuda o explicaciones sobre cómo se resolvieron estas ecuaciones, no dudes en preguntar.
Aquí están las soluciones para cada ecuación: 1. $$ \frac{2x}{3} = 15 $$ → $$ x = 22.5 $$ 2. $$ 22 - \frac{6x + 1}{3} = 5 $$ → $$ x = 8.\dot{3} $$ 3. $$ 23 - \frac{6}{x} = 3 $$ → $$ x = 0.3 $$ 4. $$ 24 - \frac{12}{x} = 4 $$ → $$ x = 0.6 $$

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