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3 x+7=2 x+4 | Numerade

Name: Problem 53, Chapter 2: Beginning and Intermediate Algebra
Uploaded: 2022-02-12T00:48:28-08:00
Duration: 29 s
Channel: Christopher Stanley
Description: 3 x+7=2 x+4

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The highest power of the variable is one, and the graph of a linear equation in two variables is a straight line. Linear equations are foundational for understanding relationships that change at a constant rate.

Properties of Equality

The properties of equality are fundamental rules that allow one to manipulate and solve equations while maintaining equality. These include adding or subtracting the same value from both sides of an equation, as well as multiplying or dividing both sides by the same nonzero number. These properties ensure that the operations performed do not alter the solution set of the equation.

Combining Like Terms

Combining like terms is the process of simplifying an algebraic expression by merging terms that have the same variable raised to the same power. This step is essential in making equations easier to solve by reducing complexity and clarifying the structure of the expression.

Isolation of Variables

Isolation of variables is a key strategy in solving equations, particularly linear equations. It involves rearranging the equation to get the variable of interest on one side and the constants on the other. This process uses the properties of equality and simplifies the equation to a form where the variable can be directly solved.

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