To find the value of \( x \) in the equation \( 1.5(x+4)-3=4.5(x-2) \), we need to solve for \( x \) step by step:
1. **Distribute the constants:**
\( 1.5(x+4) - 3 = 4.5(x-2) \)
\( 1.5x + 6 - 3 = 4.5x - 9 \)
2. **Combine like terms:**
\( 1.5x + 3 = 4.5x - 9 \)
3. **Isolate the variable terms:**
Subtract \( 1.5x \) from both sides:
\( 3 = 3x - 9 \)
Add 9 to both sides:
\( 3 + 9 = 3x \)
\( 12 = 3x \)
4. **Solve for \( x \):**
Divide by 3 on both sides:
\( x = 4 \)
Therefore, the value of \( x \) in the equation \( 1.5(x+4)-3=4.5(x-2) \) is \( x = 4 \).
