Question

solve the compound inequality.
4x + 2 < 6 and 4x + 1 > - 19
graph the solution on the number line.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Explanation:

Step1: Solve the first inequality

Subtract 2 from both sides of $4x + 2<6$:
$4x+2 - 2<6 - 2$, which simplifies to $4x<4$. Then divide both sides by 4: $x < 1$.

Step2: Solve the second inequality

Subtract 1 from both sides of $4x + 1>-19$:
$4x+1 - 1>-19 - 1$, which simplifies to $4x>-20$. Then divide both sides by 4: $x>-5$.

Answer:

The solution of the compound - inequality is $-5 < x < 1$. On the number line, there is an open circle at - 5, an open circle at 1, and the line is shaded between them.