# How do you graph and solve |5-x| +5>=5?

Aug 27, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{5}$ from each side of the inequality to isolate the absolute value function:

$\left\mid 5 - x \right\mid + 5 - \textcolor{red}{5} \ge 5 - \textcolor{red}{5}$

$\left\mid 5 - x \right\mid + 0 \ge 0$

$\left\mid 5 - x \right\mid \ge 0$

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

$- 0 \ge 5 - x \ge 0$

$0 \ge 5 - x \ge 0$

$- \textcolor{red}{5} + 0 \ge - \textcolor{red}{5} + 5 - x \ge - \textcolor{red}{5} + 0$

$- 5 \ge 0 - x \ge - 5$

$- 5 \ge - x \ge - 5$

$\textcolor{b u e}{- 1} \times - 5 \textcolor{red}{\le} \textcolor{b u e}{- 1} \times - x \textcolor{red}{\le} \textcolor{b u e}{- 1} \times - 5$

$5 \textcolor{red}{\le} x \textcolor{red}{\le} 5$

Or

$x \ge 5$ and $x \le 5$

Because $x$ can be greater than or less than $5$ and it can be equal to $5$ the solution is $x$ is the set of all Real Numbers: $\left\{\mathbb{R}\right\}$.

In other words, $x$ can be any value and the inequality will be true.

The graph will look like a solid shaded area:

graph{x>=-10005}