# What is the negative root of the equation abs(2x+3)=11?

Apr 27, 2018

$- 7$.

#### Explanation:

$| 2 x + 3 | = 11$.

$\therefore 2 x + 3 = \pm 11$.

$2 x + 3 = + 11 \Rightarrow 2 x = 11 - 3 = 8 \Rightarrow x = 4 > 0$.

If, $2 x + 3 = - 11 , \text{ then, "2x=-14," giving, } x = - 7 < 0$.

$\therefore x = - 7$, is the desired root!

Aug 4, 2018

$x = - 7$

#### Explanation:

This equation can be interpreted as

$2 x + 3 = 11$ and $2 x + 3 = - 11$, but we are concerned with only the negative root, as the question says.

We have

$2 x + 3 = - 11$

We can subtract $3$ from both sides to get

$2 x = - 14$

Lastly, we can divide both sides by $2$ to isolate $x$. We get

$x = - 7$

Hope this helps!