# How do you solve and write the following in interval notation:  [(2x − 6)/(x+1)] ≤1?

Dec 2, 2017

$x \setminus \rightarrow \left[- \setminus \infty , 7\right]$

#### Explanation:

We can isolate for $x$ by algebraically manipulating the inequality:

$\setminus \frac{2 x - 6}{x + 1} \setminus \le q 1$

Multiply both sides by $x + 1$:

$\setminus \implies 2 x - 6 \setminus \le q 1 \left(x + 1\right)$

Subtract $x$ from both sides:

$\setminus \implies x - 6 \setminus \le q 1$

Add $6$ to both sides:

$\setminus \implies x \setminus \le q 7$

This means $x$ can take on a value of any that $7$ or less, which can be expressed in interval notation as:

$\left[- \setminus \infty , 7\right]$