https://file.aiquickdraw.com/mathbot/file/1726613877128lwerjm1e.jpg

The equation provided is:

\[
\frac{4}{5}x - \frac{3}{2} = -\frac{1}{2}x - 6
\]

Let's solve this for \(x\).

### Step 1: Eliminate fractions by multiplying through by the least common denominator (LCD). 
The denominators are 5 and 2, so the LCD is 10. Multiply every term by 10:

\[
10 \left(\frac{4}{5}x\right) - 10 \left(\frac{3}{2}\right) = 10 \left(-\frac{1}{2}x\right) - 10(6)
\]

This simplifies to:

\[
8x - 15 = -5x - 60
\]

### Step 2: Combine like terms.
Move all terms involving \(x\) to one side of the equation, and constants to the other:

\[
8x + 5x = -60 + 15
\]

This simplifies to:

\[
13x = -45
\]

### Step 3: Solve for \(x\).

\[
x = \frac{-45}{13}
\]

Thus, the solution is:

\[
x = \frac{-45}{13}
\]

Would you like further details or have any questions about the solution? Here are some related problems for practice:

1. Solve \( \frac{3}{4}x - \frac{5}{6} = -\frac{1}{3}x + 7 \).
2. Solve \( 2x - 3 = \frac{5}{2}x + 8 \).
3. Solve \( \frac{7}{3}x - \frac{9}{5} = \frac{4}{3}x + 1 \).
4. Solve \( \frac{6}{x} + 3 = \frac{4}{x} + 7 \).
5. Solve \( \frac{5}{x+1} - 2 = \frac{3}{x+2} \).

**Tip:** When dealing with fractions, multiplying through by the least common denominator helps to eliminate them quickly!

Solve for x: (4/5)x - (3/2) = -(1/2)x - 6

Learn how to solve the linear equation (4/5)x - (3/2) = -(1/2)x - 6. This problem involves simplifying fractions, combining like terms, and solving for x. Suitable for students in Grades 8-10.

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