Question

Solve for the indicated variable. $$ 7 x-(2 x+3)=x-2 $$

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

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 27

Instant Answer

Solved by Expert Amy Jiang

06/30/2020

Step 1

$$ 7x - 2x - 3 = x - 2 $$ Show more…

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Solve for the indicated variable. $$ 7 x-(2 x+3)=x-2 $$

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Key Concepts

Linear Equations

Linear equations are algebraic expressions that involve the unknown variable(s) to the first power, and can be solved through a series of algebraic manipulations. They form the foundation of algebra and require balancing methods to isolate the variable and find its value.

Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses. This property is useful when simplifying expressions by removing parentheses, thus making it easier to combine like terms and simplify the equation.

Combining Like Terms

Combining like terms involves adding or subtracting terms in an expression that have the same variable parts. This simplification step is crucial in reducing the equation to a simpler form, making it easier to isolate and solve for the variable.

Isolation of Variables

Isolation of variables is the process of manipulating an equation so that one side contains only the unknown variable. This is achieved by performing equivalent operations on both sides of the equation, which allows one to solve for the variable directly.

Properties of Equality

The properties of equality state that performing the same mathematical operation on both sides of an equation will not change its equality. These properties are fundamental in solving equations as they justify the steps taken to isolate the variable and simplify the equation.

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