Question

graph each inequality on a number line.

1. ( x < -4 ) \t\t\t\t34. ( x geq 5 )

1. ( x leq 2 ) \t\t\t\t36. ( x geq 1 )

1. ( -6 < x ) \t\t\t\t38. ( 0 geq x )

1. ( 9 leq x ) \t\t\t\t40. ( -1 > x )

Explanation:

Step1: Graph $x < -4$

Draw an open circle at $-4$, shade all numbers to the left.

Step2: Graph $x \geq 5$

Draw a closed circle at $5$, shade all numbers to the right.

Step3: Graph $x \leq 2$

Draw a closed circle at $2$, shade all numbers to the left.

Step4: Graph $x \geq 1$

Draw a closed circle at $1$, shade all numbers to the right.

Step5: Graph $-6 < x$ (rewrite as $x > -6$)

Draw an open circle at $-6$, shade all numbers to the right.

Step6: Graph $0 \geq x$ (rewrite as $x \leq 0$)

Draw a closed circle at $0$, shade all numbers to the left.

Step7: Graph $9 \leq x$ (rewrite as $x \geq 9$)

Draw a closed circle at $9$, shade all numbers to the right.

Step8: Graph $-1 > x$ (rewrite as $x < -1$)

Draw an open circle at $-1$, shade all numbers to the left.

Answer:

1. For $x < -4$: Open circle at $-4$, shade left of $-4$.
2. For $x \geq 5$: Closed circle at $5$, shade right of $5$.
3. For $x \leq 2$: Closed circle at $2$, shade left of $2$.
4. For $x \geq 1$: Closed circle at $1$, shade right of $1$.
5. For $-6 < x$: Open circle at $-6$, shade right of $-6$.
6. For $0 \geq x$: Closed circle at $0$, shade left of $0$.
7. For $9 \leq x$: Closed circle at $9$, shade right of $9$.
8. For $-1 > x$: Open circle at $-1$, shade left of $-1$.