Question

Solve for the indicated variable. $$ 2(x-1)+3=x-3(x+1) $$

   Solve for the indicated variable.
$$
2(x-1)+3=x-3(x+1)
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 23

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Solved by Expert Amy Jiang

06/30/2020

Step 1

$$ 2(x-1)+3=x-3(x+1) $$ $$ 2x-2+3=x-3x-3 $$ Show more…

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Solve for the indicated variable. $$ 2(x-1)+3=x-3(x+1) $$

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Key Concepts

Solving Linear Equations

Solving linear equations is the process of isolating the variable on one side of the equation to determine its value. This typically involves applying operations such as distribution, combining like terms, and inverse operations in a step-by-step manner to simplify the equation.

Distributive Property

The distributive property allows one to remove parentheses by multiplying the term outside the parentheses by each term inside the parentheses. This simplifies expressions and is critically used to expand and simplify equations before further manipulation.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable components. This process simplifies the expression, reducing it to a more manageable form, which is especially useful when solving equations.

Inverse Operations

Inverse operations are actions that reverse the effect of a given operation, such as subtraction undoing addition or division undoing multiplication. They are essential for isolating variables and solving equations by systematically reversing the operations applied to the variable.

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