Question

solve the inequality and graph the solution.
9 - 4p ≥ 1
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
<---(-5)---(-4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \( p \), we subtract 9 from both sides of the inequality \( 9 - 4p \geq 1 \). This gives us \( 9 - 4p - 9 \geq 1 - 9 \), which simplifies to \( -4p \geq -8 \).

Step2: Divide by -4 (and reverse inequality)

When dividing an inequality by a negative number, we must reverse the inequality sign. So, dividing both sides of \( -4p \geq -8 \) by -4 gives \( \frac{-4p}{-4} \leq \frac{-8}{-4} \), which simplifies to \( p \leq 2 \).

Answer:

The solution to the inequality \( 9 - 4p \geq 1 \) is \( p \leq 2 \). To graph this, we plot a closed dot at \( 2 \) (since the inequality is "greater than or equal to" or "less than or equal to", the endpoint is included) and draw an arrow to the left to represent all values of \( p \) less than or equal to \( 2 \).