High School

Which of the following inequalities is equivalent to the inequality [tex]4x^4 \leq 9x^8[/tex]?

A. [tex]x^4 \leq \frac{9}{4}x^8[/tex]
B. [tex]4x^4 \leq 9x^8[/tex]
C. [tex]4 \leq 9x^4[/tex]
D. [tex]\frac{4}{9} \leq x^4[/tex]

Answer :

Final answer:

The inequality 4x <= 9x simplifies to 0 <= x, which means that x is greater than or equal to 0. This simplification is done by subtracting 4x from both sides and then dividing by 5.

Explanation:

To find an equivalent inequality to 4x ≤ 9x, you need to subtract 4x from both sides of the inequality to isolate terms. The inequality will then become 0 ≤ 5x. If you divide both sides of the inequality by 5, we get 0 ≤ x, which means x is greater than or equal to 0. So, the correct equivalent inequality is 0 ≤ x.

Step-by-step:

  1. Subtract 4x from both sides: 4x - 4x ≤ 9x - 4x
  2. Simplify: 0 ≤ 5x
  3. Divide by 5: 0/5 ≤ x
  4. Simplify: 0 ≤ x

Learn more about Inequalities here:

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