Solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]

Verified step by step guidance

1. Distribute the -2 inside the parentheses on the left-hand side: -2(1 - x) becomes -2 + 2x. Simplify the expression inside the brackets.
2. Simplify the brackets on the left-hand side: [4 - (-2 + 2x) + 3] becomes [4 + 2 - 2x + 3]. Combine like terms inside the brackets.
3. Simplify further on the left-hand side: [4 + 2 + 3 - 2x] becomes [9 - 2x]. Multiply the entire bracket by -2.
4. On the right-hand side, distribute the -2 inside the parentheses: -2(x - 3) becomes -2x + 6. Simplify the expression inside the brackets.
5. Combine all terms on both sides of the equation, isolate x, and solve for x by performing inverse operations (addition, subtraction, division, etc.).

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In solving equations, correctly applying these rules is crucial for simplifying expressions accurately.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a set of parentheses. This property is essential for simplifying expressions and solving equations, as it helps eliminate parentheses and combine like terms effectively, making the equation easier to manage.

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 various algebraic manipulations, such as adding, subtracting, multiplying, or dividing both sides. Understanding how to manipulate equations is fundamental for arriving at the correct solution.