# How do you solve and write the following in interval notation: -2 ≤ x + 4  OR -1 + 3x > -8?

May 26, 2018

$\left[- 6 , \setminus \infty\right)$

#### Explanation:

You can rewrite $- 2 \setminus \le x + 4$ as

$- 2 - 4 \setminus \le x + 4 - 4 \setminus \implies - 6 \setminus \le x \setminus \implies x \setminus \ge - 6$

Similarly, rewrite $- 1 + 3 x \succ 8$ as

$- 1 + 3 x + 1 \succ 8 + 1 \setminus \implies 3 x \succ 7 \setminus \implies x > - \frac{7}{3}$

Since $- 6 < - \frac{7}{3}$, any number which is greater than $- \frac{7}{3}$ will automatically be greater than $- 6$. And since the OR condition requires at least one of the conditions to be true, it is sufficient to ask $x \setminus \ge - 6$

To write it in interval notation, we must find the boundaries of the desired region. We want $x$ to be greater than $- 6$, but we have no upper bound, which means it's $\setminus \infty$.

So, the interval is $\left[- 6 , \setminus \infty\right)$