1. **State the problem:** Solve the equation $$-7 + 7x - 3x = 37$$ for $$x$$. 2. **Combine like terms:** The terms with $$x$$ are $$7x$$ and $$-3x$$. Combine them: $$7x - 3x = 4x$$ So the equation becomes: $$-7 + 4x = 37$$ 3. **Isolate the term with $$x$$:** Add 7 to both sides to move the constant term: $$-7 + 4x + 7 = 37 + 7$$ $$\cancel{-7} + 4x + \cancel{7} = 44$$ $$4x = 44$$ 4. **Solve for $$x$$:** Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{44}{\cancel{4}}$$ $$x = 11$$ 5. **Final answer:** $$x = 11$$ --- **Check the solution:** Substitute $$x = 11$$ back into the original equation: 1. Substitute: $$-7 + 7(11) - 3(11) = ?$$ 2. Calculate multiplication: $$-7 + 77 - 33 = ?$$ 3. Combine terms: $$(-7 + 77) - 33 = 70 - 33 = 37$$ 4. Since the left side equals the right side (37), the solution $$x=11$$ is correct.