1. **State the problem:** Solve the equation $$7(x - 4) = -2x + 26$$ for $$x$$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses. $$7 \times x - 7 \times 4 = 7x - 28$$ So the equation becomes: $$7x - 28 = -2x + 26$$ 3. **Collect like terms:** Add $$2x$$ to both sides to get all $$x$$ terms on one side. $$7x + 2x - 28 = 26$$ $$9x - 28 = 26$$ 4. **Isolate the variable term:** Add 28 to both sides. $$9x = 26 + 28$$ $$9x = 54$$ 5. **Solve for $$x$$:** Divide both sides by 9. $$x = \frac{54}{9}$$ $$x = 6$$ **Final answer:** $$x = 6$$