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!