Solve. 10-5(3 x+1)=5(x-4)

Name: Problem 44, Chapter 2: Elementary Algebra
Uploaded: 2022-01-22T23:12:48-08:00
Duration: 57 s
Channel: James Kiss
Description: Solve. 10-5(3 x+1)=5(x-4)

Key Concepts

Linear Equations

Linear equations are algebraic expressions in which the variable(s) appear to the first power. They represent straight line relationships and can be solved by isolating the variable. This fundamental type of equation requires systematic manipulation and is central to algebra.

Distributive Property

The distributive property allows the multiplication of a term by an expression inside parentheses, converting expressions such as a(b + c) into ab + ac. This property is essential for eliminating parentheses and simplifying equations.

Combining Like Terms

Combining like terms is the process of simplifying expressions by merging terms with the same variables, which reduces the equation to a simpler form. This step aids in making the equation more manageable and leads toward isolating the variable.

Isolation of Variables

Isolation of variables refers to rearranging an equation so that all terms containing the variable are on one side and the constant terms are on the other. This often involves the use of inverse operations, allowing one to solve directly for the unknown variable.

Balancing Equations

Balancing equations involves performing the same operation on both sides of an equation to maintain equality. This principle is foundational in solving equations, ensuring that the integrity of the equation is preserved during the manipulation of terms.

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