−3z+2≤8 put on a number line using (), [], (], or [) rather than circles 

Let's solve the inequality first:

\[
-3z + 2 \leq 8
\]

1. Subtract 2 from both sides:

\[
-3z \leq 6
\]

2. Divide by -3 (remember to flip the inequality sign because we are dividing by a negative number):

\[
z \geq -2
\]

This inequality can be written as \( z \in [-2, \infty) \).

On a number line:

- We use a **square bracket** [ at -2 because \( z \geq -2 \), meaning -2 is included.
- We use a **parenthesis** ) at infinity since infinity is never included in intervals.

Thus, the number line representation is: \[ [-2, \infty) \].

Would you like more details on this, or do you have any questions?

Here are 5 related questions:

1. What is the general rule for flipping inequality signs?
2. How would you graph a strict inequality like \( z > -2 \)?
3. What happens if you divide by a positive number in an inequality?
4. How do we represent unbounded intervals like \( (-\infty, 2] \)?
5. Can inequalities be represented using set notation?

**Tip**: When dividing or multiplying both sides of an inequality by a negative number, always flip the inequality sign!

−3z+2≤8 put on a number line using (), [], (], or [) rather than circles

Learn how to solve the inequality −3z + 2 ≤ 8 and represent the solution on a number line using proper interval notation. This example covers key concepts like inequality reversal when dividing by a negative number. Suitable for students in Grades 7-9.

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