Question

Can we solve $3(c+2)+5(2 c-5) ?$ Why or why not?

   Can we solve $3(c+2)+5(2 c-5) ?$ Why or why not?

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 3, Problem 5

Instant Answer

Solved by Expert Caleb Elmore

06/30/2020

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Step 1: First, let's look at the given expression $3(c+2)+5(2 c-5)$. Show more…

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Can we solve $3(c+2)+5(2 c-5) ?$ Why or why not?

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Key Concepts

Algebraic Expressions vs. Equations

An algebraic expression is a mathematical phrase that can include numbers, variables, and operations, but it does not contain an equality sign. This means that while we can simplify an expression, we cannot 'solve' it in the same way we solve an equation. To solve something, there typically needs to be an equation with two expressions set equal to each other, allowing us to find the value of a variable.

Distributive Property

The distributive property is a fundamental principle in algebra used to expand expressions, particularly those involving parentheses. It states that multiplying a number by a sum or difference inside parentheses is equivalent to multiplying each term inside the parentheses by the number outside. This property is crucial when simplifying expressions such as the one given.

Combining Like Terms

Combining like terms is a process used in simplifying algebraic expressions, where terms with the same variable components are added or subtracted. After using the distributive property to expand the expression, like terms can be merged to produce a simplified expression, making it easier to understand or further manipulate.

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