Question

Will the sum of two linear expressions each with an x-term , always,sometimes,or never have an x-term ? Explain your reasoning

Answer 1

The sum will have an x-term sumtimes ... whenever
the x-terms alone don't add up to zero.

Examples:

-- Two linear expressions:

         y +  x
and   
         y + 2x

The sum of the x-terms alone is (x + 2x) = 3x .
So the sum of the expressions has an x-term.

         (y + x) + (y + 2x)  =  2y + 3x .
_______________________________

Two different linear expressions:

       y + 3x
and
       y - 3x

The sum of the x-terms alone is (3x - 3x) = zero.
So the sum of the expressions doesn't have an x-term.

         (y + 3x) + (y - 3x)  =  2y .