Question

(01.05 mc) which of the following is the correct graph of the compound inequality 4p + 1 > -7 and 6p + 3 < 33?

Explanation:

Step1: Solve the first inequality

Subtract 1 from both sides of $4p + 1>-7$:
$4p+1 - 1>-7 - 1$, which simplifies to $4p>-8$. Then divide both sides by 4: $p > - 2$.

Step2: Solve the second inequality

Subtract 3 from both sides of $6p + 3<33$:
$6p+3 - 3<33 - 3$, which simplifies to $6p<30$. Then divide both sides by 6: $p < 5$.

Step3: Determine the solution set

The solution of the compound - inequality is $-2 < p < 5$. On a number - line, this is represented by an open circle at $p=-2$, an open circle at $p = 5$, and the line segment between them.

Answer:

The graph with an open circle at - 2, an open circle at 5, and the line segment between them.