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Encuentre el valor de la variable 𝑥 aplicando las propiedades de la 
igualdad

Let's solve the first equation, which involves the variable \( x \):

### Equation 7: \( 4x + 3(x - 2) = 18 - x \)

1. **Distribute** the 3 on the left-hand side:
   \[
   4x + 3x - 6 = 18 - x
   \]

2. **Combine like terms** on the left-hand side:
   \[
   7x - 6 = 18 - x
   \]

3. **Add \( x \) to both sides** to eliminate the \( -x \) on the right-hand side:
   \[
   7x + x - 6 = 18
   \]
   \[
   8x - 6 = 18
   \]

4. **Add 6 to both sides** to isolate the term with \( x \):
   \[
   8x = 24
   \]

5. **Divide both sides by 8** to solve for \( x \):
   \[
   x = 3
   \]

Thus, the value of \( x \) is \( \boxed{3} \).

Would you like to go over the solution steps in more detail or have any questions? Additionally, here are some related questions to explore further:

1. How do you solve for \( x \) in a different equation, like equation 8?
2. What are the key properties of equality used in solving linear equations?
3. How can you verify your solution to ensure it's correct?
4. What happens when you have variables on both sides of the equation?
5. How does distributing work when dealing with negative coefficients?
6. Why is it important to combine like terms?
7. Can you solve equation 9 using a similar method?
8. What strategies can be used if you encounter fractions in the equation?

**Tip:** Always check your solution by substituting the value of the variable back into the original equation.

Discover how to find the value of variable x by applying properties of equality. Step-by-step solution provided for equation 4x + 3(x - 2) = 18 - x, illustrating the use of distributive property and combining like terms. Suitable for Grades 7-9.

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