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QUESTION IMAGE

solve the inequality and graph the solution. 1 > -p - 1 to draw a ray, …

Question

solve the inequality and graph the solution.
1 > -p - 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.

Explanation:

Step1: Add 1 to both sides

$$\begin{align*} 1+1&>-p - 1+1\\ 2&>-p \end{align*}$$

Step2: Multiply both sides by - 1 and reverse the inequality sign

When we multiply both sides of an inequality \(a > b\) by a negative number \(c\), the inequality sign reverses, i.e., \(ac

$$\begin{align*} 2\times(- 1)&<(-p)\times(-1)\\ -2&

which can be written as \(p > - 2\)

Answer:

The solution of the inequality \(1>-p - 1\) is \(p > - 2\). On the number - line, we plot an open circle at \(p=-2\) (because the inequality is strict, i.e., \(p
eq - 2\)) and draw a ray to the right of \(-2\) to represent all real numbers greater than \(-2\)