Question

solve the inequality lx-3l < (or equal to) 5?

Answer 1

\(|x-3| \le 5\)
With absolute values, yo break it down into 2 situations:

1) if \(x-3 \ge 0\):
\(x-3 \le 5\\
x \le 5+3 \\
x \le 8\)

2) if \(x-3 < 0\):
\(-(x-3) \le 5 \\
-x+3 \le 5\\
-x \le 2\\
x \ge -2\)

So the solution is the union of \(x \le 8\) and \(x \ge -2\) which means:
\(-2 \le x \le 8\)

Answer 2

Oh! Thank you for the help! Now it makes more sense.

Answer 3

:)