1. **Problem:** Solve the equation $14 \times (4x + 2) = 140$ algebraically. 2. **Formula and rules:** Use the distributive property to expand and then isolate $x$ by performing inverse operations step-by-step. 3. **Step 1:** Expand the left side: $$14 \times (4x + 2) = 14 \times 4x + 14 \times 2 = 56x + 28$$ 4. **Step 2:** Set the equation: $$56x + 28 = 140$$ 5. **Step 3:** Subtract 28 from both sides: $$56x + \cancel{28} - \cancel{28} = 140 - 28$$ $$56x = 112$$ 6. **Step 4:** Divide both sides by 56: $$\frac{56x}{\cancel{56}} = \frac{112}{\cancel{56}}$$ $$x = 2$$ **Final answer:** $x = 2$