What is the solution to the equation 5(2w+4)=4(2w+9)

To solve the equation \(5(2w + 4) = 4(2w + 9)\), follow these steps:

1. **Distribute the constants** on both sides:
   \[
   5 \times (2w + 4) = 10w + 20
   \]
   \[
   4 \times (2w + 9) = 8w + 36
   \]
   The equation becomes:
   \[
   10w + 20 = 8w + 36
   \]

2. **Move the variable terms** to one side by subtracting \(8w\) from both sides:
   \[
   10w - 8w + 20 = 36
   \]
   Simplify:
   \[
   2w + 20 = 36
   \]

3. **Isolate the variable** by subtracting 20 from both sides:
   \[
   2w = 16
   \]

4. **Solve for \(w\)** by dividing both sides by 2:
   \[
   w = 8
   \]

So, the solution is \(w = 8\).

Would you like any details on this process or have any questions?

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Here are 5 related questions to explore:

1. How do you solve an equation with variables on both sides?
2. What happens if there is no solution to the equation?
3. Can equations like this have more than one solution?
4. How would you solve the equation if fractions were involved?
5. What is the next step if you have an equation with parentheses and more complex expressions?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Explore how to solve the linear equation 5(2w + 4) = 4(2w + 9) with a step-by-step approach. This problem emphasizes the use of the distributive property and the basic properties of equality. Ideal for students in Grades 6-8.

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