Math Problem Statement

1≥x/3

Solution

The inequality 1x31 \geq \frac{x}{3} can be solved by isolating xx. Here's how:

Step-by-Step Solution:

  1. Start with the given inequality: 1x31 \geq \frac{x}{3}

  2. Multiply both sides by 3 to eliminate the denominator. Since 3 is positive, the inequality direction remains the same: 3x3 \geq x

  3. Rewrite this inequality for clarity: x3x \leq 3

Final Answer:

x3x \leq 3

This means that xx can take any value less than or equal to 3.


Would you like more details or have any questions?

Related Questions:

  1. How would the solution change if the inequality was 1x31 \leq \frac{x}{3}?
  2. Can you explain how the solution changes if the denominator is negative?
  3. What is the graphical representation of x3x \leq 3?
  4. How can you test a value to see if it satisfies x3x \leq 3?
  5. How does multiplying or dividing by a variable affect inequality solutions?

Tip: Always check the direction of the inequality when multiplying or dividing by negative numbers!

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Math Problem Analysis

Mathematical Concepts

Inequalities
Algebra

Formulas

Inequality solving: Multiply both sides by a constant

Theorems

Properties of inequalities (multiplying/dividing by positive numbers)

Suitable Grade Level

Grades 7-9