Consider the equation x+3=3(x+1)−2x. Is this equation a linear equation? I would say to my students that an equation in 1 variable is linear when it can be simplified to the form ax=b where a≠0. Also, I would mention that a linear equation in 1 variable has only 1 solution. Therefore, I would say that the equation x+3=3(x+1)−2x is not linear because it can be reduced to 0x=0 which has infinite solutions. However, a colleague whose research area is algebra says that a linear equation is one that only involves polynomials of degree 1. Therefore, the equation x+3=3(x+1)−2x is linear. Then, according to the definition of my colleague, the equation x−x=0 is linear as well. I was thinking that maybe a third possibility is that according to the definition of "linear equation" only equations of the form "expression=0" can be classified as linear or non-linear. In this case, the equation x+3=3(x+1)−2x is not linear nor non-linear, but the equation x−x=0 would be linear. What should be the definition for "linear equation" in 1 variable suitable for a math course?

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Consider the equation x+3=3(x+1)−2x. Is this equation a linear equation?  I would say to my students that an equation in 1 variable is linear when it can be simplified to the form ax=b where a≠0. Also, I would mention that a linear equation in 1 variable has only 1 solution. Therefore, I would say that the equation x+3=3(x+1)−2x is not linear because it can be reduced to 0x=0 which has infinite solutions.  However, a colleague whose research area is algebra says that a linear equation is one that only involves polynomials of degree 1. Therefore, the equation x+3=3(x+1)−2x is linear. Then, according to the definition of my colleague, the equation x−x=0 is linear as well.  I was thinking that maybe a third possibility is that according to the definition of &quot;linear equation&quot; only equations of the form &quot;expression=0&quot; can be classified as linear or non-linear. In this case, the equation x+3=3(x+1)−2x is not linear nor non-linear, but the equation x−x=0 would be linear.  What should be the definition for &quot;linear equation&quot; in 1 variable suitable for a math course?

lucratifar1 · Accepted Answer

However, a colleague whose research area is algebra says that a linear equation is one that only involves polynomials of degree 1. Therefore, the equation 0=0(on simplification)  is linear. Then, according to the definition of my colleague, the equation  is linear as well.  The problem is &quot;The degree of a zero polynomial is not defined or −∞&quot;. So saying that zero polynomial has degree 1 is little vague as 0≡0x≡0x2≡0x3≡…..  What should be the definition for &quot;linear equation&quot; in 1 variable suitable for a math course?  A linear polynomial p(x)=ax+b,a≠0 when equated to a real number α(say i.e. p(x)=α is called a linear equation.

surgescasjag · Accepted Answer

Thanks for answer!

Consider the equation x+3=3(x+1)-2x. Is this equation a linear equation? I would say to my

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