Question

Solve the equation. $$3(x+2)=5(x-6)$$

   Solve the equation.
$$3(x+2)=5(x-6)$$

Precalculus: Graphs and Models

Precalculus: Graphs and Models

Raymond A. Barnett,… 3rd Edition

Chapter 2, Problem 21

Instant Answer

Solved by Expert Ernest Castorena

06/19/2020

Step 1

Step 1: First, distribute the 3 and 5 on both sides of the equation: $$3x + 6 = 5x - 30$$ Show more…

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Solve the equation. $$3(x+2)=5(x-6)$$

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Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term within a set of parentheses. This is a crucial step for eliminating parentheses and simplifying the equation.

Balance Property of Equality

The balance property of equality states that what you do to one side of an equation must be done to the other side to maintain equality. This principle is essential to accurately solving equations without changing their solutions.

Isolation of the Variable

Isolation of the variable is the process of manipulating the equation so that the variable appears on one side and all the constant terms on the other. This often involves addition, subtraction, multiplication, or division to solve for the variable.

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. In problems like this, the goal is to find the value of the variable that makes the equation true.

Combining Like Terms

Combining like terms involves merging terms that have the same variable factors. This helps simplify the equation into a more manageable form by reducing the number of distinct terms.

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