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.