1. **State the problem:** Solve for $x$ in the equation $$8.6 + 5.6x - 1.5 = 40.7.$$\n\n2. **Simplify the equation:** Combine like terms on the left side: $$8.6 - 1.5 = 7.1,$$ so the equation becomes $$7.1 + 5.6x = 40.7.$$\n\n3. **Isolate the term with $x$:** Subtract 7.1 from both sides: $$5.6x = 40.7 - 7.1 = 33.6.$$\n\n4. **Solve for $x$:** Divide both sides by 5.6: $$x = \frac{33.6}{5.6} = 6.$$\n\n**Final answer:** $$x = 6.$$