Math Problem Statement

Solve for x and graph the solution on the number line: 4 >= 2x

Solution

The inequality given in the image is:

42x4 \geq 2x

Solving for xx:

  1. Start by dividing both sides of the inequality by 2 to isolate xx: 422x2\frac{4}{2} \geq \frac{2x}{2} Simplifying: 2xorx22 \geq x \quad \text{or} \quad x \leq 2

So, the solution is: x2x \leq 2

Inequality Notation:

x2x \leq 2

Graphing on the Number Line:

  • Since x2x \leq 2, we place a filled circle on 2, indicating that 2 is included in the solution.
  • We shade the number line to the left of 2, indicating all values less than or equal to 2 are part of the solution.

Would you like further details on this solution or the graph? Here are some related questions:

  1. How do you handle inequalities with negative coefficients?
  2. What happens when dividing both sides of an inequality by a negative number?
  3. Can you solve a compound inequality and graph it?
  4. How do you express inequality solutions in interval notation?
  5. What is the difference between strict inequalities (<<, >>) and inclusive inequalities (\leq, \geq)?

Tip: When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Number Line Graphing

Formulas

Division of inequality: If a >= bx, then a/b >= x

Theorems

Inequality Rule: Dividing or multiplying both sides of an inequality by a positive number keeps the inequality direction unchanged.

Suitable Grade Level

Grades 6-8