Final answer:
To solve the inequality 5/3(2x^2) - 10 ≥ 2x^2(2/3x^2), distribute, simplify, and isolate the variable x. Factor out common terms and change the direction of the inequality when dividing by a negative number.
Step-by-step explanation:
To solve the inequality 5/3(2x^2) - 10 ≥ 2x^2(2/3x^2), we need to simplify and isolate the variable x. First, distribute and simplify the terms on both sides of the equation:
(10/3)x^2 - 10 ≥ (4/3)x^4
Next, subtract (10/3)x^2 from both sides:
- 10 ≥ (4/3)x^4 - (10/3)x^2
Now, let's focus on the right side of the equation and factor out a common term, which is x^2:
- 10 ≥ (4/3)x^2(x^2 - 10/3)
Finally, divide both sides by (x^2 - 10/3) and change the direction of the inequality since we are dividing by a negative number:
(4/3)x^2(x^2 - 10/3) ≤ 10
This is the simplified form of the inequality.