Question

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

Answer 1

False.

Explanation:

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`