graph the compound inequality. write the solution using interval notation. x < -3 or x > 2

planation:

Step1: Analyze the first inequality (x < - 3)

For (x < - 3), on the number - line, we draw an open circle at (x=-3) (because the inequality is strict, (x\neq - 3)) and shade to the left of (-3). In interval notation, this part is ((-\infty,-3)).

Step2: Analyze the second inequality (x>2)

For (x > 2), on the number - line, we draw an open circle at (x = 2) (because the inequality is strict, (x\neq2)) and shade to the right of (2). In interval notation, this part is ((2,\infty)).

Step3: Combine the two intervals for the 'or' compound inequality

Since the compound inequality is (x < - 3) or (x>2), we take the union of the two intervals.

Answer:

The interval notation for the solution of the compound inequality (x < - 3) or (x>2) is ((-\infty,-3)\cup(2,\infty)).