Question

graph: 5 < x
graph: 1/4 ≥ x
graph: x < -1

Explanation:

Step1: Graph \(5 < x\)

For \(5 < x\), which can also be written as \(x>5\). On a number line, we use an open circle at \(x = 5\) (because \(x\) is not equal to \(5\)) and draw an arrow to the right (since \(x\) is greater than \(5\)).

Step2: Graph \(\frac{1}{4}\geq x\)

For \(\frac{1}{4}\geq x\) or \(x\leq\frac{1}{4}\). On a number line, we use a closed circle at \(x=\frac{1}{4}\) (because \(x\) can be equal to \(\frac{1}{4}\)) and draw an arrow to the left (since \(x\) is less than or equal to \(\frac{1}{4}\)).

Step3: Graph \(x < - 1\)

For \(x < - 1\). On a number line, we use an open circle at \(x=-1\) (because \(x\) is not equal to \(-1\)) and draw an arrow to the left (since \(x\) is less than \(-1\)).

Answer:

For \(5 < x\): Open - circle at \(5\), arrow to the right.
For \(\frac{1}{4}\geq x\): Closed - circle at \(\frac{1}{4}\), arrow to the left.
For \(x < - 1\): Open - circle at \(-1\), arrow to the left.