# How do you solve and write the following in interval notation: |2x-1|+7>=1?

Jul 14, 2017

The solution set for $| 2 x - 1 | + 7 \ge 1$ is $\left\{x \in \mathbb{R}\right\}$

#### Explanation:

Subtract 7 from both sides

$| 2 x - 1 | \ge - 6$

The left hand side is always considered as positive. So it can not be equal to $- 6$ Thus $| 2 x - 1 | + 7 \ge 1$ is wrong. It should read $| 2 x - 1 | + 7 > 1$

The form of $| 2 x - 1 | + 7 > 1$ means that all real values of x will make the inequality be true.

The solution set for $| 2 x - 1 | + 7 \ge 1$ is $\left\{x \in \mathbb{R}\right\}$

To illustrate this, I shall substitute $\frac{1}{2}$ for x:

$| 2 \left(\frac{1}{2}\right) - 1 | + 7 \ge 1$

$| 0 | + 7 \ge 1$

$7 \ge 1$

This inequality is true and I have chosen the value for x where any other value will only make the number on the left side become greater. Therefore, the solution set is all real values of x.