Math Problem Statement
Solve for x and graph the solution on the number line below: 36 ≤ 4x
Solution
Let's solve the inequality:
Step 1: Solve for
To isolate , divide both sides of the inequality by 4:
This simplifies to:
Step 2: Inequality Notation
The inequality notation is:
Step 3: Graph on the Number Line
On the number line, you will plot a closed dot at (because the inequality includes , as indicated by the "greater than or equal to" symbol ). Then, shade the region to the right of 9, indicating all values greater than or equal to 9.
Final Answer:
- Inequality Notation:
- Graph: Closed dot at , with shading to the right of 9.
Would you like further details on this, or do you have any questions?
Here are 5 related questions to expand your understanding:
- How do you graph inequalities with "<" or ">" on a number line?
- What happens if you divide an inequality by a negative number?
- How would the graph change if the inequality were ?
- Can you explain how solving inequalities differs from solving equations?
- How would you solve a compound inequality involving two inequality signs?
Tip: Always flip the inequality sign when multiplying or dividing both sides by a negative number!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Formulas
Solving linear inequalities by dividing both sides by a constant
Theorems
Properties of inequalities
Suitable Grade Level
Grades 7-9