I have some question to ask you that explain to me and remove my confusion. 1.The book said that we call for those equations linear that have first degree power or general forms of linear equations now my question is that we call for those kind of equations linear that have general form of linear equation or can change to general form or other forms of linear equations form example can we call 10x=5 linear or square root of (y−9)=10 linear? 2.Can those rational and radical equations that can be manipulated to linear forms called linear equations like the examples above? 3.Are all first degree one variable equations linear?

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I have some question to ask you that explain to me and remove my confusion.    1.The book said that we call for those equations linear that have first degree power or general forms of linear equations now my question is that we call for those kind of equations linear that have general form of linear equation or can change to general form or other forms of linear equations form example can we call 10x=5 linear or square root of (y−9)=10 linear?    2.Can those rational and radical equations that can be manipulated to linear forms called linear equations like the examples above?    3.Are all first degree one variable equations linear?

Rebekah Irvine · Accepted Answer

To define linear equations, we need to understand linear functions of a variable. Let us assume a function f:R→R, such that    f(ax1+bx2)=af(x1)+bf(x2)    For all x1,x2,a,b∈R    Any function with this property is a linear function. Now, we can define a linear equation to be    f(x)=0    where f is a linear function in x.    Now, when you look at functions like    f(x)=10x−5    This is clearly not a linear function, and hence the equation f(x)=0 per se is not a linear equation, but with a bit of manipulation, we can define a g(x)=10−5x, such that the following is true    if x solves g(x) = 0⇒x solves f(x) = 0    And hence the equations that you have mentioned though are not linear, they are analogous to a linear equation, and hence they share the same solution set. This gives us a tool to solve a non-linear equation using a corresponding transformation to get a linear equation, which is easier to solve

I have some question to ask you that explain to me and remove my confusion. 1.The book said th

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