https://file.aiquickdraw.com/mathbot/file/1725370292799lcpf3lf6.jpg

The expression in the image is:

\[
\frac{9x + 5}{14} + \frac{8x - 7}{7} - \frac{18x + 11}{28} = \frac{5}{4}
\]

Let's solve this step by step.

### Step 1: Simplify the fractions where possible.
1. \(\frac{8x - 7}{7}\) simplifies to \( \frac{8x}{7} - 1\).
2. \(\frac{18x + 11}{28}\) does not simplify directly, but it's already expressed in the simplest form.

### Step 2: Find a common denominator.
- The denominators are 14, 7, and 28. The least common multiple (LCM) of these is 28. 

Let's rewrite all terms with a denominator of 28:

1. \(\frac{9x + 5}{14} = \frac{2(9x + 5)}{28} = \frac{18x + 10}{28}\)
2. \(\frac{8x - 7}{7} = \frac{4(8x - 7)}{28} = \frac{32x - 28}{28}\)
3. \(\frac{18x + 11}{28}\) is already over 28.

Now the equation becomes:

\[
\frac{18x + 10}{28} + \frac{32x - 28}{28} - \frac{18x + 11}{28} = \frac{5}{4}
\]

### Step 3: Combine the fractions on the left-hand side.
Since the denominators are the same, combine the numerators:

\[
\frac{(18x + 10) + (32x - 28) - (18x + 11)}{28} = \frac{5}{4}
\]

Simplify the numerator:

\[
\frac{18x + 10 + 32x - 28 - 18x - 11}{28} = \frac{5}{4}
\]

\[
\frac{32x - 29}{28} = \frac{5}{4}
\]

### Step 4: Solve for \(x\).

Cross-multiply to solve for \(x\):

\[
4(32x - 29) = 5(28)
\]

\[
128x - 116 = 140
\]

Add 116 to both sides:

\[
128x = 256
\]

Finally, divide by 128:

\[
x = 2
\]

### Conclusion:
The solution is \(x = 2\).

Would you like more details or have any questions? Here are 5 related questions for further practice:

1. How would you solve the equation if the constants were different?
2. What happens if the fractions have different denominators?
3. Can you verify the solution by substituting \(x = 2\) back into the original equation?
4. How would you handle an equation with more than three fractions?
5. How would you solve a similar equation with a quadratic term?

**Tip:** Always simplify the fractions first to make it easier to find a common denominator.

Solve the equation: (9x + 5)/14 + (8x - 7)/7 - (18x + 11)/28 = 5/4

Learn how to solve linear equations involving fractions with detailed step-by-step instructions. This example equation, (9x + 5)/14 + (8x - 7)/7 - (18x + 11)/28 = 5/4, demonstrates key algebraic techniques, including finding a common denominator and cross multiplication, making it suitable for students in Grades 9-10.

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