Solve the compound inequality. \[ -5 x \leq-15 \text { or } 6 x-23 \geq 19 \] Select the correct choice below and, if nece

Step 1 ：The given inequality is a compound inequality. It can be solved by isolating the variable 'x' in each inequality.

Step 2 ：For the first inequality, we can isolate 'x' by dividing all parts by -5. Remember that when we divide or multiply an inequality by a negative number, the inequality sign flips. So, \(-5x \leq -15\) becomes \(x \geq 3\).

Step 3 ：For the second inequality, we can isolate 'x' by first adding 23 to both sides, and then dividing by 6. So, \(6x - 23 \geq 19\) becomes \(x \geq 7\).

Step 4 ：Since the original inequality is an 'or' inequality, the solution is the union of the solutions to the two inequalities. So, the solution to the compound inequality is \(x \geq 3\) or \(x \geq 7\).

Step 5 ：Final Answer: The solution to the compound inequality is \(x \geq 3\) or \(x \geq 7\). This can be written in interval notation as \(\boxed{[3, \infty) \cup [7, \infty)}\). However, since [7, \infty) is a subset of [3, \infty), we can simplify this to just \(\boxed{[3, \infty)}\).