1. **State the problem:** Solve the equation $7(7-x)=6+2x$ for $x$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses. $$7 \times 7 - 7 \times x = 6 + 2x$$ $$49 - 7x = 6 + 2x$$ 3. **Collect like terms:** Move all terms involving $x$ to one side and constants to the other. $$49 - 7x = 6 + 2x$$ Add $7x$ to both sides: $$49 = 6 + 2x + 7x$$ $$49 = 6 + 9x$$ 4. **Isolate the variable term:** Subtract 6 from both sides. $$49 - 6 = 9x$$ $$43 = 9x$$ 5. **Solve for $x$:** Divide both sides by 9. $$\frac{\cancel{43}}{\cancel{9}} = x$$ Since 43 and 9 have no common factors, the fraction stays as is: $$x = \frac{43}{9}$$ **Final answer:** $$x = \frac{43}{9}$$