Math Problem Statement

Solve for x and graph the solution on the number line below: 36 ≤ 4x

Solution

Let's solve the inequality:

364x36 \leq 4x

Step 1: Solve for xx

To isolate xx, divide both sides of the inequality by 4:

3644x4\frac{36}{4} \leq \frac{4x}{4}

9x9 \leq x

This simplifies to:

x9x \geq 9

Step 2: Inequality Notation

The inequality notation is:

x9x \geq 9

Step 3: Graph on the Number Line

On the number line, you will plot a closed dot at x=9x = 9 (because the inequality includes x=9x = 9, as indicated by the "greater than or equal to" symbol \geq). Then, shade the region to the right of 9, indicating all values greater than or equal to 9.

Final Answer:

  • Inequality Notation: x9x \geq 9
  • Graph: Closed dot at x=9x = 9, 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:

  1. How do you graph inequalities with "<" or ">" on a number line?
  2. What happens if you divide an inequality by a negative number?
  3. How would the graph change if the inequality were 4x364x \leq 36?
  4. Can you explain how solving inequalities differs from solving equations?
  5. 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!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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