Question

solve the compound inequality. 3x - 1 ≤ - 19 or 4x + 3 > 19. graph the solution on the number line.

Explanation:

Step1: Solve the first - inequality

Solve $3x - 1\leq - 19$. Add 1 to both sides: $3x\leq - 19 + 1$, so $3x\leq - 18$. Then divide both sides by 3: $x\leq - 6$.

Step2: Solve the second - inequality

Solve $4x+3>19$. Subtract 3 from both sides: $4x>19 - 3$, so $4x>16$. Then divide both sides by 4: $x > 4$.

Step3: Combine the solutions

The compound inequality is an "or" inequality. The solution set is $x\leq - 6$ or $x>4$.

Answer:

The solution set is $x\leq - 6$ or $x>4$. To graph on a number line: Draw a closed circle at $x = - 6$ and shade to the left for $x\leq - 6$, and draw an open circle at $x = 4$ and shade to the right for $x>4$.