https://file.aiquickdraw.com/mathbot/file/1725377797768z9sdibez.jpg

The equation provided is:

\[
\frac{5x + 4}{2} + 7 = 14
\]

Let's solve for \( x \):

1. **Isolate the fraction:**

   Subtract 7 from both sides of the equation:
   \[
   \frac{5x + 4}{2} = 14 - 7
   \]
   \[
   \frac{5x + 4}{2} = 7
   \]

2. **Eliminate the denominator:**

   Multiply both sides by 2 to eliminate the denominator:
   \[
   5x + 4 = 7 \times 2
   \]
   \[
   5x + 4 = 14
   \]

3. **Isolate \( x \):**

   Subtract 4 from both sides:
   \[
   5x = 14 - 4
   \]
   \[
   5x = 10
   \]

4. **Solve for \( x \):**

   Divide both sides by 5:
   \[
   x = \frac{10}{5}
   \]
   \[
   x = 2
   \]

So, the solution is \( x = 2 \).

Would you like any details or have any questions?

Here are some related questions:

1. What is the next step if we have \( \frac{5x + 4}{2} + 7 = 15 \)?
2. How would you solve the equation if the right side was different, say \( \frac{5x + 4}{2} + 7 = 20 \)?
3. Can you solve \( \frac{3x + 6}{4} + 2 = 8 \) similarly?
4. What would happen if the coefficient of \( x \) was different, like \( 4x + 4 \) instead of \( 5x + 4 \)?
5. How do you check if your solution is correct for this type of equation?

**Tip:** Always double-check your steps, especially when isolating terms or eliminating fractions, to avoid small mistakes that could lead to incorrect solutions.

Solve the equation (5x + 4) / 2 + 7 = 14.

Learn how to solve the linear equation (5x + 4) / 2 + 7 = 14 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equation solving and basic operations. Suitable for students in Grades 6-8.

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