Question

solve the compound inequality.
3x - 5 ≤ -14 or 4x - 2 > 14
graph the solution on the number line.

Explanation:

Step1: Solve \(3x - 5\leq - 14\)

Add \(5\) to both sides:
\(3x-5 + 5\leq - 14+5\)
\(3x\leq - 9\)
Divide both sides by \(3\):
\(x\leq - 3\)

Step2: Solve \(4x - 2>14\)

Add \(2\) to both sides:
\(4x-2 + 2>14 + 2\)
\(4x>16\)
Divide both sides by \(4\):
\(x>4\)

Answer:

The solution of the compound inequality \(3x - 5\leq - 14\) or \(4x - 2>14\) is \(x\leq - 3\) or \(x>4\). On the number - line, we have a closed circle at \(x = - 3\) (since \(x=-3\) is included in \(x\leq - 3\)) and an arrow to the left for \(x\leq - 3\), and an open circle at \(x = 4\) (since \(x = 4\) is not included in \(x>4\)) and an arrow to the right for \(x>4\).