Math Problem Statement

If

⋅ (9x) ≥ 3, which of the following inequalities must be true?

Solution

The given inequality is:

(9x)3(9x) \geq 3

To solve for xx, divide both sides of the inequality by 9:

x39x \geq \frac{3}{9}

Simplifying:

x13x \geq \frac{1}{3}

Therefore, the inequality that must be true is:

x13x \geq \frac{1}{3}

Would you like further details or have any questions?

Here are 5 related questions for further practice:

  1. Solve the inequality 5x285x - 2 \geq 8.
  2. What is the solution to 4x+7194x + 7 \leq 19?
  3. Solve x342\frac{x}{3} - 4 \leq 2.
  4. What happens to the inequality if you multiply both sides by a negative number?
  5. Solve 12x3612x \geq 36.

Tip: When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Divide both sides of inequality: x ≥ 3/9

Theorems

Properties of inequalities

Suitable Grade Level

Grades 6-8