We are tasked with solving the inequality:

"Seven more than five sixths of a number is more than negative three."

Let's define the unknown number as $x$. We can then translate the problem into an inequality.

1. "Five sixths of a number" is written as $\frac{5}{6}x$.
2. "Seven more than that" means we add 7: $\frac{5}{6}x + 7$.
3. The inequality "is more than negative three" is written as $> -3$.

So, the inequality becomes: $\frac{5}{6}x + 7 > -3$

Step 1: Isolate the term with $x$

Subtract 7 from both sides: $\frac{5}{6}x > -3 - 7$ $\frac{5}{6}x > -10$

Step 2: Eliminate the fraction

Multiply both sides of the inequality by 6 to get rid of the denominator: $5x > -60$

Step 3: Solve for $x$

Divide both sides by 5: $x > -12$

Final Answer:

The solution to the inequality is $x > -12$.

Would you like further details or clarifications on this solution?

Here are 5 related questions:

1. What happens if the inequality were "less than" instead of "more than"?
2. How would you solve this if the number were represented as a decimal?
3. What if the coefficient of $x$ were a fraction other than $\frac{5}{6}$?
4. Can you rewrite this inequality in terms of absolute values?
5. What if we change the constant from 7 to a different number?

Tip: When solving inequalities, remember that if you multiply or divide by a negative number, the inequality sign flips.