Question

Solve the inequality and graph its solution. \(p-12 \geq-1\)

Short answer

The solution to the inequality is \(p \geq 11\). It is graphed with a filled-in circle at 11 and an arrow pointing to the right on a number line.

Step-by-step solution

Set up the inequality

Our initial inequality is \(p - 12 \geq -1\). The goal now is to solve the inequality for \(p\).

Solve the inequality

To solve for \(p\), add 12 to both sides of the equation. So, \(p = -1 + 12\), which simplifies to \(p \geq 11\).

Graph the solution

The solution to this inequality is \(p \geq 11\). This means any number larger or equal to 11 is a solution to the inequality. On a number line, this would be graphed with a filled-in circle at 11 (since \(p\) can equal 11) and an arrow pointing to the right (since all numbers larger than 11 are solutions).