We are given the equation:

\[
-\frac{1}{2} = -\frac{4}{7}u - \frac{5}{4}
\]

Let's solve for \( u \).

### Step 1: Eliminate the constants from the right side
To begin, add \(\frac{5}{4}\) to both sides to move the constant term to the left:

\[
-\frac{1}{2} + \frac{5}{4} = -\frac{4}{7}u
\]

### Step 2: Simplify the left side
We need a common denominator to add the fractions on the left-hand side. The least common denominator (LCD) of 2 and 4 is 4:

\[
-\frac{1}{2} = -\frac{2}{4}
\]

Now, add the fractions:

\[
-\frac{2}{4} + \frac{5}{4} = \frac{3}{4}
\]

So, the equation becomes:

\[
\frac{3}{4} = -\frac{4}{7}u
\]

### Step 3: Solve for \( u \)
To isolate \( u \), multiply both sides of the equation by the reciprocal of \(-\frac{4}{7}\), which is \(-\frac{7}{4}\):

\[
u = \frac{3}{4} \times -\frac{7}{4}
\]

Multiply the fractions:

\[
u = \frac{3 \times -7}{4 \times 4} = \frac{-21}{16}
\]

Thus, the solution is:

\[
u = -\frac{21}{16}
\]

Let me know if you want any further details or clarifications!

### Related Questions:
1. How do you multiply fractions?
2. What is the process for finding a common denominator?
3. How do you handle negative signs when solving equations?
4. How can you check if a solution to an equation is correct?
5. What are the steps to isolate a variable in a multi-term equation?

### Tip:
When dealing with fractions, always simplify at the earliest possible step to make calculations easier.

Explore how to solve the linear equation -1/2 = -4/7u - 5/4, including steps to eliminate constants, add fractions, and isolate the variable u. This detailed guide covers key algebraic concepts such as fraction operations and inverse multiplication. Suitable for students in Grades 8-10.

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