Question

write the sentence as an inequality. a number m is more than $-7 \frac{2}{3}$ or at most $-10$. inequality: $m > -\frac{23}{3}$ or $m \leq -10$ graph the inequality.

Explanation:

Step1: Analyze \( m > -\frac{23}{3} \) (i.e., \( m > -7\frac{2}{3} \))

For the inequality \( m > -7\frac{2}{3} \), we use an open circle at \( -7\frac{2}{3} \) (since \( m \) is strictly greater, not equal) and draw an arrow to the right (indicating all numbers greater than \( -7\frac{2}{3} \)).

Step2: Analyze \( m \leq -10 \)

For the inequality \( m \leq -10 \), we use a closed circle at \( -10 \) (since \( m \) can be equal to \( -10 \)) and draw an arrow to the left (indicating all numbers less than or equal to \( -10 \)).

Graph Description:

• For \( m > -7\frac{2}{3} \) (or \( m > -\frac{23}{3} \)): Place an open circle at \( -7\frac{2}{3} \) (which is between \( -8 \) and \( -7 \), closer to \( -7 \)) and draw an arrow pointing to the right.
• For \( m \leq -10 \): Place a closed circle at \( -10 \) and draw an arrow pointing to the left.

(Visually, on the number line provided, mark a closed dot at -10 with an arrow left, and an open dot at \( -7\frac{2}{3} \) (around -7.666...) with an arrow right.)

Answer:

(Inequality):
\( m > -\frac{23}{3} \) or \( m \leq -10 \)

(For the graph, as described above, implement the closed circle at -10 (arrow left) and open circle at \( -7\frac{2}{3} \) (arrow right) on the number line.)