Question

solve the inequality and graph the solution.
$p + 7 \leq -1$
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
<--|--(-8)--|--(-6)--|--(-4)--|--(-2)--|--0--|--2--|--4--|--6--|--8--|--10--->

Explanation:

Step1: Subtract 7 from both sides

To solve for \( p \), we subtract 7 from both sides of the inequality \( p + 7 \leq -1 \). This gives us \( p + 7 - 7 \leq -1 - 7 \).

Step2: Simplify both sides

Simplifying the left side, \( p + 7 - 7 \) becomes \( p \). Simplifying the right side, \( -1 - 7 \) is \( -8 \). So we have \( p \leq -8 \).

For graphing: The endpoint is at -8 (closed circle because the inequality is "less than or equal to"), and the arrow points to the left (since \( p \) is less than or equal to -8, we include all numbers less than -8).

Answer:

The solution to the inequality is \( p \leq -8 \). For the graph, plot a closed circle at -8 and draw an arrow to the left.