Question

Solve each equation. $$2[x-(4+2 x)+3]-2 x+2$$

   Solve each equation.
$$2[x-(4+2 x)+3]-2 x+2$$

Precalculus

Margaret L. Lial,… 4th Edition

Chapter 1, Problem 17

Instant Answer

Solved by Expert Sarah X

08/03/2020

Step 1

Step 1: Start by simplifying the expression inside the brackets: \[ x - (4 + 2x) + 3 \] Distribute the negative sign: \[ x - 4 - 2x + 3 \] Combine like terms: \[ (x - 2x) + (-4 + 3) = -x - 1 \] Show more…

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Solve each equation. $$2[x-(4+2 x)+3]-2 x+2$$

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Key Concepts

Distributive Property

This is an algebraic property that allows one to multiply a single term by each term inside a parenthesis, transforming expressions like a(b + c) into ab + ac. It is critical in simplifying expressions and solving equations where multiplication is distributed over addition or subtraction within grouped terms.

Combining Like Terms

This is the process of merging terms in an algebraic expression that have the same variable parts, effectively reducing the expression to a simpler form. By grouping coefficients of identical variables and consolidating constant terms, one can simplify and solve linear expressions and equations more efficiently.

Order of Operations

This concept dictates the proper sequence in which operations should be performed within an expression to ensure accurate results. It typically follows the rules of parentheses, exponents, multiplication and division, and finally addition and subtraction, ensuring that expressions are evaluated consistently and correctly.

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