Solve each linear equation. See Examples 1–3. 2 [x - (4 + 2x) + 3] = 2x + 2

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Start by simplifying the expression inside the brackets on the left side: \(x - (4 + 2x) + 3\). Remember to distribute the negative sign across the terms inside the parentheses.

Rewrite the left side after simplification, then multiply the entire bracketed expression by 2 as indicated by the coefficient outside the brackets.

Set the simplified left side equal to the right side of the equation, which is \(2x + 2\).

Collect like terms on each side of the equation to isolate the variable terms on one side and constants on the other side.

Solve for \(x\) by dividing both sides of the equation by the coefficient of \(x\) to find the value of the variable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses. For example, a(b + c) = ab + ac. This is essential for simplifying expressions before solving equations.

Combining Like Terms

Combining like terms involves adding or subtracting terms with the same variable and exponent to simplify expressions. This step reduces complexity and helps isolate the variable in an equation.

Solving Linear Equations

Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating the variable using inverse operations such as addition, subtraction, multiplication, or division.

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