Beginning Algebra With Applications, Chapter 2, Review Exercises, Section Review Exercises, Problem 34

Simplify $2x + 3[ x - 2(4-2x)]$

$\begin{equation} \begin{aligned} &= 2x +3 [x - 2(4) - (-2)(2x)] && \text{Use the Distributive Property}\\ \\ &= 2x + 3[x - 2(4) + (2 \cdot 2) x] && \text{Use the Associative Property of Multiplication to group factors}\\ \\ &= 2x + 3[x - 8 + 4x] && \text{Simplify}\\ \\ &= 2x + 3[5x - 8] && \text{Combine like terms}\\ \\ &= 2x +3(5x) - 3(8) && \text{Again, by using the Distributive Property}\\ \\ &=2x + (3 \cdot 5)x - 3(8) && \text{Use again the Associative Property of Multiplication to group factors}\\ \\ &= 2x + 15x - 24 && \text{Simplify}\\ \\ &= 17x - 24 && \text{Combine like terms} \end{aligned} \end{equation}$