Question

Part 1: Show the work to solve |5x – 2| greater than or equal to 8

Part 2: Describe the graph of the solution in words

Answer 1

\[abs (5x-2) \ge 8\] In order for this to be true, either 5x-2 is greater than or equal to 8, OR 5x-2 is less than or equal to -8. So:
\[5x-2 \ge 8 -> 5x \ge 10 -> x \ge 2\] OR
\[5x-2 \le -8 -> 5x \le -6 -> x \le -6/5\]

Answer 2

\[\left| 5x-2 \right| \ge 8 \implies 5x-2 \ge 8~~or~~5x-2 \le -8\]\[\implies 5x \ge 10~~or~~5x \le -6\]\[\implies x \ge 2~~or~~x \le \frac{-6}{5}\]

Answer 3

Describe the graph please

Answer 4

The solution set is \[(-\infty,-\frac{6}{5}] \cup [2, \infty)\]so the graph is a number line with brackets facing outward (toward plus/minus infinity) at -5/6 and 2.