Question

for problems 4–6, graph the solutions to the inequality on the number line.

1. ( x > 0 )

1. ( y < -3 )

1. ( 5 > z )

the number lines in problems 7 and 8 each show the solutions to an inequality. for each problem, write two inequalities that each represent the solutions graphed on the number line. use ( x ) as the variable.
7.

8.

Explanation:

Step1: Graph $x>0$

• Draw an open circle at $0$, shade all numbers to the right of $0$ on the number line.

Step2: Graph $y<-3$

• Draw an open circle at $-3$, shade all numbers to the left of $-3$ on the number line.

Step3: Rewrite and graph $5>z$

Rewrite as $z<5$. Draw an open circle at $5$, shade all numbers to the left of $5$ on the number line.

Step4: Write inequalities for problem 7

The graph has an open circle at $5$ and shades left: $x<5$ and $5>x$.

Step5: Write inequalities for problem 8

The graph has an open circle at $-2$ and shades right: $x>-2$ and $-2

Answer:

1. For $x>0$: Open circle at 0, shade right.
2. For $y<-3$: Open circle at -3, shade left.
3. For $5>z$ (or $z<5$): Open circle at 5, shade left.
4. For problem 7: $x<5$, $5>x$
5. For problem 8: $x>-2$, $-2