Question

solve the inequality.
p + \frac{1}{4} \geq 2
the solution is p \geq \frac{7}{4}.
graph the solution.

Explanation:

Step1: Isolate the variable p

Subtract $\frac{1}{4}$ from both sides of the inequality $p+\frac{1}{4}\geq2$.
$p+\frac{1}{4}-\frac{1}{4}\geq2 - \frac{1}{4}$

Step2: Calculate the right - hand side value

$2-\frac{1}{4}=\frac{8}{4}-\frac{1}{4}=\frac{8 - 1}{4}=\frac{7}{4}$, so $p\geq\frac{7}{4}$.

Step3: Graph the solution

The inequality $p\geq\frac{7}{4}$ means $p$ is greater than or equal to $\frac{7}{4}$. On a number line, we use a closed - circle (because of the $\geq$ sign) at $\frac{7}{4}$ (which is $1.75$) and draw an arrow to the right. Among the given arrow - circle options, the correct one is a closed - circle with an arrow pointing to the right.

Answer:

The solution of the inequality is $p\geq\frac{7}{4}$. The correct graphing option is the one with a closed - circle and an arrow pointing to the right. (Since the number line provided in the problem is not correctly scaled for $\frac{7}{4}$, but conceptually the correct graphical representation is a closed - circle at $\frac{7}{4}$ and an arrow to the right).