Question

question 3 of 14, step 2 of 2
consider the following linear inequality.
9p - 2 < 1 + 11p
step 2 of 2: graph the solution set.
pressing the buttons will create an interval with the indicated endpoint type. the interval is graphed by moving the endpoints to the desired values. to remove graphed intervals, use the clear button. to indicate infinity or negative infinity, drag an open endpoint to the end of the number line.
-∞ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 ∞

Explanation:

Step 1: Solve the inequality

First, we start with the inequality \(9p - 2<1 + 11p\).
Subtract \(9p\) from both sides:
\(9p-9p - 2<1 + 11p-9p\), which simplifies to \(- 2<1 + 2p\).
Then subtract 1 from both sides: \(-2 - 1<1-1 + 2p\), so \(-3<2p\).
Divide both sides by 2: \(\frac{-3}{2}-\frac{3}{2}=-1.5\).

Step 2: Graph the solution set

On the number - line, we place an open circle at \(-1.5\) (because the inequality is \(p > - 1.5\), not \(p\geq - 1.5\)) and draw an arrow to the right to represent all values of \(p\) that are greater than \(-1.5\).

Answer:

The solution set is \(p>-\frac{3}{2}\), and on the number - line, an open circle at \(-\frac{3}{2}\) and an arrow to the right.