Solve for 
\[a\].
 
 
\[-\dfrac{1}4a-4=\dfrac{7}4a-3\]

To solve for \( a \) in the equation

\[
-\frac{1}{4}a - 4 = \frac{7}{4}a - 3
\]

we can proceed with the following steps:

### Step 1: Eliminate Fractions
Multiply both sides of the equation by 4 to clear the fractions:

\[
4 \left(-\frac{1}{4}a - 4\right) = 4 \left(\frac{7}{4}a - 3\right)
\]

This simplifies to:

\[
-a - 16 = 7a - 12
\]

### Step 2: Move Variables to One Side
Add \( a \) to both sides to get all terms involving \( a \) on one side:

\[
-16 = 8a - 12
\]

### Step 3: Move Constants to the Other Side
Add 12 to both sides:

\[
-16 + 12 = 8a
\]

\[
-4 = 8a
\]

### Step 4: Solve for \( a \)
Divide both sides by 8:

\[
a = -\frac{4}{8}
\]

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

### Solution
The solution is:

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

Would you like further details, or have any questions?

Here are some related questions to explore further:
1. How do you solve equations with multiple fractions?
2. What other methods can simplify equations without clearing fractions?
3. How can you verify solutions to linear equations?
4. What if there are variables on both sides without constants?
5. How do you apply this approach to inequalities?

**Tip:** When working with fractions in equations, clearing the fractions early can simplify the solving process.

Solve for \(a\).

\[-\frac{1}{4}a - 4 = \frac{7}{4}a - 3\]

Learn how to solve the linear equation -1/4a - 4 = 7/4a - 3 with step-by-step guidance. This solution demonstrates clearing fractions, isolating variables, and simplifying terms, making it suitable for students in Grades 7-9.

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