Question

solve the compound inequality. 4x + 1 < 1 or 4x + 1 > 21 graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 1 from both sides of $4x + 1<1$.
$4x+1 - 1<1 - 1$, which simplifies to $4x<0$. Then divide both sides by 4: $x < 0$.

Step2: Solve the second inequality

Subtract 1 from both sides of $4x + 1>21$.
$4x+1 - 1>21 - 1$, which simplifies to $4x>20$. Then divide both sides by 4: $x>5$.

Answer:

The solution is $x < 0$ or $x>5$. On the number - line, an open circle is drawn at $x = 0$ and the line is shaded to the left of 0, and an open circle is drawn at $x = 5$ and the line is shaded to the right of 5.