Solve the inequality and graph the solution.

11 minus five sixths x less than 711−56x<7

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Part 1

Solve the inequality. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The inequality has a solution that is not all real numbers. The solution is 

enter your response here.

​(Type an inequality. Simplify your​ answer.)

B.

The solution of the inequality is all real numbers.

C.

The inequality has no solution.

To solve the inequality \(11 - \frac{5}{6}x < 7\), we need to isolate \(x\). Here’s how we do it step-by-step:

### Step 1: Subtract 11 from both sides of the inequality
\[
11 - \frac{5}{6}x - 11 < 7 - 11
\]
Simplifying both sides:
\[
-\frac{5}{6}x < -4
\]

### Step 2: Multiply both sides by \(-1\) to eliminate the negative sign
When multiplying or dividing by a negative number, we must flip the inequality sign:
\[
\frac{5}{6}x > 4
\]

### Step 3: Multiply both sides by \(\frac{6}{5}\) to solve for \(x\)
\[
x > 4 \times \frac{6}{5}
\]
\[
x > \frac{24}{5}
\]
\[
x > 4.8
\]

Thus, the solution to the inequality is \(x > 4.8\).

### Answer:
A. The inequality has a solution that is not all real numbers. The solution is \(x > 4.8\).

### Graphing the Solution:
To graph the solution \(x > 4.8\), you would:

1. Draw a number line.
2. Place an open circle at \(x = 4.8\) to indicate that 4.8 is not included in the solution.
3. Shade the number line to the right of 4.8 to show that all numbers greater than 4.8 are included in the solution.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What would the solution be if the inequality was \(11 - \frac{5}{6}x > 7\)?
2. How do you solve inequalities involving fractions differently from those with whole numbers?
3. Why do we flip the inequality sign when multiplying or dividing by a negative number?
4. How would the solution change if the inequality was \(11 - \frac{5}{6}x \leq 7\)?
5. Can you give an example of a real-world scenario where this type of inequality might be used?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Solve the inequality and graph the solution: 11 - (5/6)x < 7. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Learn how to solve and graph the linear inequality 11 - (5/6)x < 7. This problem involves algebraic concepts, including manipulating inequalities and applying the rule for reversing the inequality when multiplying or dividing by a negative. Suitable for students in Grades 7-10.

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