True or False? If #(2x-3)(x+5)=8#, then either #2x-3=8# or #x+5=8#.

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Answer 1 · 2017-08-19T14:51:19

False.

You know that

#(2x - 3)(x+5) = 8#

Assuming that you have

#2x - 3 = 8#

you can say that this requires

#x + 5 = 1#

since you need

#overbrace( (2x-3))^(color(blue)(=8)) * overbrace((x+5))^(color(blue)(=1)) = 8#

This implies that you have

#2x - 3 = 8 implies x = 11/2 = 5.5#

which will make

#x + 5 = 5.5 + 5 != 1#

Now, let's assume that

#x + 5 = 8 #

This implies that you must have

#2x - 3 = 1#

since you need

#overbrace( (2x-3))^(color(blue)(=1)) * overbrace((x+5))^(color(blue)(=8)) = 8#

In this case, you have

#x + 5 = 8 implies x = 3#

which will make

#2x - 3 = 2 * 3 - 3 != 1#

Therefore, you can say that for

#(2x-3)(x+5) = 8#

you cannot have

#2x - 3 = 8 " " or " " x + 5 = 8#