Question

solve the inequality.

$p+\frac{1}{4}geq2$

the solution is

graph the solution

Explanation:

Step1: Subtract \(\frac{1}{4}\) from both sides

$$p+\frac{1}{4}-\frac{1}{4}\geq2 - \frac{1}{4}$$

Step2: Simplify the right - hand side

$$p\geq\frac{8}{4}-\frac{1}{4}=\frac{8 - 1}{4}=\frac{7}{4}=1.75$$

Answer:

\(p\geq\frac{7}{4}\) (or \(p\geq1.75\))

To graph the solution:

• Locate the point \(1.75\) on the number line.
• Since the inequality is \(\geq\), we use a closed circle at \(1.75\) (because \(p = 1.75\) is part of the solution).
• Then draw an arrow to the right (because \(p\) can be greater than \(1.75\) as well).