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Part 1

Other than a no solution​ set, use interval notation to express the solution set and then graph the solution set on a number line.

2 minus StartFraction x Over 3 EndFraction greater than 42−x3>4




Let's solve the inequality \( 2 - \frac{x}{3} > 4 \) step by step.

### Step 1: Isolate the term with \(x\).
Subtract 2 from both sides of the inequality:

\[
2 - \frac{x}{3} - 2 > 4 - 2
\]

This simplifies to:

\[
-\frac{x}{3} > 2
\]

### Step 2: Solve for \(x\).
Multiply both sides by \(-3\) to eliminate the fraction. **Note:** When multiplying by a negative number, the inequality sign reverses:

\[
x < -6
\]

### Step 3: Express the solution in interval notation.
The solution \(x < -6\) can be written in interval notation as:

\[
(-\infty, -6)
\]

### Step 4: Graph the solution set.
- On a number line, plot an open circle at \(-6\) to indicate that \(-6\) is not included in the solution.
- Shade everything to the left of \(-6\), since the solution includes all values less than \(-6\).

#### Would you like a graph of this solution or need further clarifications?

### 5 Related Questions:
1. How do you solve inequalities with fractions?
2. What does reversing the inequality sign mean when multiplying by a negative number?
3. How is interval notation related to inequalities?
4. How do you graph different types of inequality solutions?
5. What are the steps to solving compound inequalities?

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

Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 2 minus StartFraction x Over 3 EndFraction greater than 42−x3>4

Learn how to solve the inequality 2 - x/3 > 4 step by step, express the solution in interval notation, and graph it on a number line. This tutorial covers key algebraic concepts such as inequality manipulation and interval notation. Suitable for students in Grades 7-9.

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