Question

Solve the equations. $$ 7(w-2)=-14-3 w $$

   Solve the equations.
$$
7(w-2)=-14-3 w
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 9, Problem 73

Instant Answer

Solved by Expert Erika Bustos

04/03/2022

Step 1

Step 1: First, distribute the 7 in the equation $7(w-2)=-14-3w$ to get $7w-14=-14-3w$. Show more…

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Solve the equations. $$ 7(w-2)=-14-3 w $$

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Key Concepts

Properties of Equality

The properties of equality, such as adding, subtracting, multiplying, or dividing both sides of an equation by the same number, enable the transformation of equations while preserving their equivalence. These properties are critical for systematically solving equations.

Linear Equations

A linear equation is an algebraic statement involving a variable with a power of one, meaning its graph is a straight line. Solving such equations entails finding the value of the variable that makes the equation true.

Distributive Property

The distributive property allows one to multiply a single term by each term within a parenthetical expression. This property is essential for simplifying expressions and transforming equations into a form where like terms can be combined.

Combining Like Terms

Combining like terms means merging terms that have the same variable part to simplify an expression. This process is a fundamental step in reducing an equation to its simplest form.

Isolating the Variable

Isolating the variable involves applying algebraic operations to ensure the unknown appears alone on one side of the equation. This technique is central to solving linear equations.

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