Solve each equation. 4[2x-(3-x)+5] = -6x - 28

Verified step by step guidance

1. Start by simplifying the expression inside the brackets: \(4[2x - (3 - x) + 5] = -6x - 28\). First, distribute the negative sign inside the parentheses: \(2x - 3 + x + 5\).
2. Combine like terms inside the brackets: \(2x + x - 3 + 5\) simplifies to \(3x + 2\).
3. Rewrite the equation with the simplified bracket: \(4(3x + 2) = -6x - 28\).
4. Distribute the 4 across the terms inside the parentheses: \(4 \times 3x + 4 \times 2 = 12x + 8\).
5. Set up the equation \(12x + 8 = -6x - 28\) and then solve for \(x\) by moving all \(x\) terms to one side and constants to the other side.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term outside the parentheses by each term inside the parentheses. For example, a(b + c) = ab + ac. This property is essential for simplifying expressions like 4[2x - (3 - x) + 5] before solving the equation.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions and makes solving equations easier. For instance, 2x and -x can be combined to get x.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating the variable on one side using inverse operations like addition, subtraction, multiplication, or division. The goal is to simplify the equation step-by-step until the variable is alone.