Question

Solve each linear equation. $$2(x-1)+3=x-3(x+1)$$

   Solve each linear equation.
$$2(x-1)+3=x-3(x+1)$$

Precalculus

Robert Blitzer 6th Edition

Chapter 0, Problem 10

Instant Answer

Solved by Expert James Kiss

08/18/2021

Step 1

Step 1: First, distribute the 2 and -3 on both sides of the equation: \[2x - 2 + 3 = x - 3x - 3\] Show more…

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Solve each linear equation. $$2(x-1)+3=x-3(x+1)$$

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Key Concepts

Properties of Equality

The properties of equality, such as the addition, subtraction, multiplication, and division properties, allow you to manipulate both sides of an equation equally without changing the solution set. These properties ensure that the equality remains valid while you work to isolate the variable and solve the equation.

Isolating the Variable

Isolating the variable means rearranging an equation so that the variable term is by itself on one side. This step is crucial in solving equations because it allows you to determine the value of the variable by performing inverse operations on both sides of the equation.

Distributive Property

The distributive property allows you to multiply a term by each term within a parenthesis, transforming an expression like a(b + c) into ab + ac. This property is essential for eliminating parentheses in algebraic expressions and is frequently used when simplifying and solving equations.

Combining Like Terms

Combining like terms involves simplifying an equation by adding or subtracting terms that have the same variable raised to the same power. This process reduces the equation to a simpler form, making it easier to identify and isolate variables when solving the equation.

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