Math Problem Statement
Solution
We are given the inequality:
To solve this inequality:
Step 1: Eliminate the fraction
Multiply both sides of the inequality by . Note that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses.
Step 2: Graph the solution
On the number line, the solution is represented by an open circle at and an arrow pointing to the right, indicating all values greater than .
Final Solution:
The solution is , 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:
- How would the graph change if the inequality were ?
- What happens if we multiply or divide by a negative number when solving inequalities?
- How can you check if your solution to an inequality is correct?
- How does solving linear inequalities differ from solving linear equations?
- 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