−3z>3
−
3
z
>
3
Step 1 of 2 :  Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

If all real numbers satisfy the inequality, select All Real Numbers. If no real number satisfies the inequality, select No Solution.

Selecting one of the alternative options will replace the entered value(s) with the selected value. Otherwise, the entered answer is used.

Answer

Let's solve the inequality \(-3z > 3\) step by step.

### Step 1: Isolate the variable \(z\).

The inequality is given as:
\[
-3z > 3
\]

To isolate \(z\), we need to divide both sides of the inequality by \(-3\). However, when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign.

\[
z < \frac{3}{-3}
\]

\[
z < -1
\]

### Final Answer:
The solution to the inequality is:
\[
z < -1
\]

So, the correct answer is \( z < -1 \).

Would you like any further details or explanations on this topic?

Here are 5 related questions:
1. What happens to the inequality sign when you multiply or divide by a negative number?
2. How would the solution change if the inequality was \(3z > 3\)?
3. What is the graphical representation of \(z < -1\) on a number line?
4. Can you solve a similar inequality \( -2x > 6 \)?
5. What would the solution be if the inequality was \( -3z \geq 3 \)?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number in an inequality.

-3z > 3. Solve the linear inequality for the given variable.

Learn how to solve the linear inequality -3z > 3 with a clear step-by-step guide. This problem covers essential algebraic concepts, including linear inequalities and the rule for reversing inequality signs when working with negative numbers. Suitable for students in Grades 7-9.

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