Question #bbd86

1 Answer
mimi
Nov 2, 2017

Infinitely many solutions! See below.

Explanation:

Isolate #x#:

#-4x-7+10x=-7+6x#
#6x-7=-7+6x# [Combine like terms.]
#-7=-7# [Subtract 6x from both sides.]

Notice that #x# got completely eliminated from the equation, leaving you with a constant equaling another constant.

When you get a number equaling a number, you can either draw one of two conclusions:
number#!=#number #-># NO SOLUTION
number#=#number #-># INFINITELY MANY SOLUTIONS

Since #-7# is the same (or equal to) #-7#, we can conclude that there are INFINITELY MANY SOLUTIONS, which means ANY real number substituted for #x# will make the equation true.

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