seven more than five sixths of a number is more than negative three

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.

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

Learn how to solve the inequality where seven more than five sixths of a number is more than negative three. This step-by-step guide covers key algebraic concepts, including inequality solving and fraction operations, suitable for students in Grades 6-8.

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