Which equations are linear equations in x ? A. 3 x+x-2=0 B. 12=x^2 C. 9 x-4=9 D. 3 x+2 y=6

Name: Problem 7, Chapter 1: Intermediate Algebra
Uploaded: 2022-02-09T06:33:14-08:00
Duration: 2 min 33 s
Channel: Anas Venkitta
Description: Which equations are linear equations in x ? A. 3 x+x-2=0 B. 12=x^2 C. 9 x-4=9 D. 3 x+2 y=6

step 1 In the given question, four equations have been given to us and we are asked to find which one o

Which equations are linear equations in x ? A. 3 x+x-2=0 B....

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Key Concepts

Linear Equation

A linear equation is one in which the variable(s) appear only to the first power and there are no products of variable terms. This property ensures that the graph of the equation is a straight line when plotted, reflecting a constant rate of change.

Degree

The degree of a term in an algebraic equation is the exponent of the variable. For an equation to be linear with respect to a variable, that variable's highest exponent must be one, which distinguishes linear equations from quadratic or higher degree equations.

Standard Form

Expressing an equation in its standard form, such as ax + b = 0 or ax + by = c, can clarify whether an equation is linear. This form explicitly shows that the variable is multiplied by a constant and added or subtracted by another constant.

Variable Isolation

Determining if an equation is linear in a specific variable involves checking that the variable appears only on a first-degree level and that no non-linear operations, such as multiplication by itself or other functions, are applied to it.

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