Question

Solve for the indicated variable. $$ 5 p+6(p+7)=3(p+2) $$

   Solve for the indicated variable.
$$
5 p+6(p+7)=3(p+2)
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 25

Instant Answer

Solved by Expert Amy Jiang

06/30/2020

Step 1

$$ 5p + 6p + 42 = 3p + 6 $$ Show more…

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Solve for the indicated variable. $$ 5 p+6(p+7)=3(p+2) $$

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Key Concepts

Isolating the Variable

Isolating the variable means rearranging the equation using inverse operations so that the variable stands alone on one side of the equation. This process is crucial for solving equations and finding the value of the variable.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is essential for simplifying algebraic expressions, reducing complexity, and making it easier to isolate the variable.

Linear Equations

A linear equation is an equation of the first degree, meaning the variable appears only in the first power and graphs as a straight line. Understanding linear equations is foundational because it sets the stage for solving equations where the variable is manipulated using algebraic operations.

Distributive Property

The distributive property is a key algebraic principle that allows you to multiply a single term by each term within parentheses. This property is important for expanding expressions and simplifying equations, especially when variables appear inside grouped terms.

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