Let the unknown number be $x$. Based on the problem, we can form the inequality:

$-3x - 8 > 7$

Step 1: Simplify the inequality

Add 8 to both sides to isolate the term involving $x$: $-3x > 15$

Step 2: Solve for $x$

Divide both sides by $-3$, remembering to reverse the inequality sign because we are dividing by a negative number: $x < -5$

Step 3: Interpret the solution

The number $x$ must be less than -5. Therefore, any number less than $-5$ could satisfy this inequality.

Example values

Some possible values for $x$ are: $x = -6, -7, -10, \text{etc.}$

Verify with a sample number

Take $x = -6$: $-3(-6) - 8 = 18 - 8 = 10, \quad 10 > 7 \quad \text{(True)}.$

Would you like further clarification or a graphical representation of the solution?

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1. How do you solve linear inequalities involving negative coefficients?
2. Why does dividing by a negative number reverse the inequality?
3. Can you graph the inequality $x < -5$?
4. What are other examples of numbers satisfying $x < -5$?
5. How would the solution change if the inequality was $-3x - 8 < 7$?

Tip: Always reverse the inequality sign when multiplying or dividing by a negative number!