Question

graph the following inequalities on the number lines below.
a) ( x geq 0 )
b) ( x < 1 )

Explanation:

Step1: Analyze the inequality \(x\geq0\)

For \(x\geq0\), the endpoint at \(x = 0\) is included (since the inequality is non - strict, \(\geq\)). So, we use a solid circle at \(x = 0\). The values of \(x\) are greater than or equal to \(0\), so the arrow should point to the right.

Step2: Analyze the inequality \(x<1\)

For \(x<1\), the endpoint at \(x = 1\) is not included (since the inequality is strict, \(<\)). So, we use an open circle at \(x = 1\). The values of \(x\) are less than \(1\), so the arrow should point to the left.

Answer:

a) On the number line, place a solid circle at \(0\) and draw an arrow to the right.
b) On the number line, place an open circle at \(1\) and draw an arrow to the left.