In Exercises 99–106, solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

Verified step by step guidance

1. Start by simplifying the expression inside the innermost parentheses: $4(x-3)$. Distribute the 4 to both terms inside the parentheses.
2. Simplify the expression $4(x-3)-5$ by subtracting 5 from the result of the distribution.
3. Next, simplify the expression \{2x - [result from previous step]\} by distributing the negative sign across the terms inside the brackets.
4. Combine like terms on the left side of the equation: $4x+13-[resultfrompreviousstep]$.
5. Finally, set the simplified left side equal to the right side $2(x-6)$ and solve for $x$ by isolating $x$ on one side of the equation.

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential for simplifying expressions where a term is multiplied by a sum or difference. In the given equation, applying the distributive property will help in expanding terms like 2(x - 6) and 4(x - 3) effectively.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. This concept is crucial in solving equations, as it allows for the reduction of complex expressions into simpler forms, making it easier to isolate the variable.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, and division. Understanding this concept is fundamental to arriving at the solution for the given equation.