Your teacher solved the equation 4x+1=22+x. unfortunately, due to messy handwriting you are not sure if the solution is 2,7,or8 describe how you can find the solution without solving the equation again

You can use the arcane mathematical process known as "checking".

-- Take a number, any number.

-- Write the number you chose in place of 'x' in the equation.

-- If the equation is then true, then the number you chose
    is the solution.   If not, then it's not.

                       4 x  +  1  =  22  +  x

Try 2:              4(2) +  1  =  22  + (2)
                         8    +  1  =  22  +  2
                               9      =      24       <== I don't think so.
                                                                 2 is not the solution.

Try 8:              4(8)  +  1  =  22  + (8)
                        32    +  1  =  22  +  8
                                33    =      30       <== I don't think so.
                                                                  8 is not the solution.   

Try 7:              4(7)  +  1  =  22  + (7)
                         28   +  1  =  22  +  7
                               29     =      29       <== Yay !
                                                                  7 is the solution ! 

Idon’t know actually is more difficult