1. **State the problem:** Solve the equation $ (4+6)(4+6x) = 25 - 3.5(x+4) $ for $x$. 2. **Simplify the left side:** Calculate $4+6=10$, so the equation becomes: $$ 10(4+6x) = 25 - 3.5(x+4) $$ 3. **Distribute on both sides:** $$ 10 \times 4 + 10 \times 6x = 25 - 3.5x - 3.5 \times 4 $$ $$ 40 + 60x = 25 - 3.5x - 14 $$ 4. **Simplify the right side:** $$ 40 + 60x = 11 - 3.5x $$ 5. **Bring all $x$ terms to one side and constants to the other:** $$ 60x + 3.5x = 11 - 40 $$ $$ 63.5x = -29 $$ 6. **Solve for $x$ by dividing both sides by 63.5:** $$ x = \frac{-29}{63.5} $$ 7. **Simplify the fraction:** $$ x = \frac{\cancel{-29}}{\cancel{63.5}} = -\frac{29}{63.5} $$ 8. **Calculate decimal value:** $$ x \approx -0.4567 $$ **Final answer:** $$ x \approx -0.4567 $$