Math Problem Statement

Solve \( \frac{x}{-3} < 8 \). Graph the solution.

Solution

We are given the inequality:

x3<8\frac{x}{-3} < 8

To solve this inequality:

Step 1: Eliminate the fraction

Multiply both sides of the inequality by 3-3. Note that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses.

x>8×3x > 8 \times -3

x>24x > -24

Step 2: Graph the solution

On the number line, the solution x>24x > -24 is represented by an open circle at 24-24 and an arrow pointing to the right, indicating all values greater than 24-24.

Final Solution:

The solution is x>24x > -24, which should be graphed accordingly.

Would you like more details on the steps involved, or do you have any questions?


Here are 5 related questions for further understanding:

  1. How would the graph change if the inequality were x38\frac{x}{-3} \leq 8?
  2. What happens if we multiply or divide by a negative number when solving inequalities?
  3. How can you check if your solution to an inequality is correct?
  4. How does solving linear inequalities differ from solving linear equations?
  5. Can this inequality solution be represented in interval notation?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Graphing

Formulas

Multiplication of both sides of an inequality by a negative number

Theorems

Rule of inequalities: Reversing the sign when multiplying or dividing by a negative number

Suitable Grade Level

Grades 7-9