1. **State the problem:** Simplify the expression $x + 4 \cdot x - 2$. 2. **Recall the order of operations:** Multiplication comes before addition and subtraction. 3. **Apply multiplication:** Calculate $4 \cdot x$ which is $4x$. 4. **Rewrite the expression:** Now the expression is $x + 4x - 2$. 5. **Combine like terms:** $x$ and $4x$ are like terms, so add their coefficients: $1x + 4x = 5x$. 6. **Final simplified expression:** $5x - 2$. This is the simplified form of the original expression.