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

Aug 19, 2017

False.

#### Explanation:

You know that

$\left(2 x - 3\right) \left(x + 5\right) = 8$

Assuming that you have

$2 x - 3 = 8$

you can say that this requires

$x + 5 = 1$

since you need

${\overbrace{\left(2 x - 3\right)}}^{\textcolor{b l u e}{= 8}} \cdot {\overbrace{\left(x + 5\right)}}^{\textcolor{b l u e}{= 1}} = 8$

This implies that you have

$2 x - 3 = 8 \implies x = \frac{11}{2} = 5.5$

which will make

$x + 5 = 5.5 + 5 \ne 1$

Now, let's assume that

$x + 5 = 8$

This implies that you must have

$2 x - 3 = 1$

since you need

${\overbrace{\left(2 x - 3\right)}}^{\textcolor{b l u e}{= 1}} \cdot {\overbrace{\left(x + 5\right)}}^{\textcolor{b l u e}{= 8}} = 8$

In this case, you have

$x + 5 = 8 \implies x = 3$

which will make

$2 x - 3 = 2 \cdot 3 - 3 \ne 1$

Therefore, you can say that for

$\left(2 x - 3\right) \left(x + 5\right) = 8$

you cannot have

$2 x - 3 = 8 \text{ " or " } x + 5 = 8$