Solve the following inequalities: A) 3x2 + 6 " ">= 12 - 2x2 B) 4x − 2 < 2 C) 2x − 5 < 5

Here's a check of your solutions:

A) $3x^2 + 6 \ge 12 - 2x^2$
❌ Incorrect.
Your first step of collecting like terms is correct:
$3x^2 + 2x^2 \ge 12 - 6$
$5x^2 \ge 6$
However, you incorrectly simplified $5x^2$ to $5x$. This is a quadratic inequality, not a linear one.
The correct solution involves taking the square root of both sides, remembering both positive and negative roots:
$x^2 \ge \frac{6}{5}$
$x \le -\sqrt{\frac{6}{5}}$ or $x \ge \sqrt{\frac{6}{5}}$
Which simplifies to $x \le -\frac{\sqrt{30}}{5}$ or $x \ge \frac{\sqrt{30}}{5}$.

B) $4x - 2 < 2$
✅ Correct.
Your steps are accurate:
$4x < 2 + 2$
$4x < 4$
$x < 1$

C) $2x - 5 < 5$
✅ Correct.
Your steps are accurate:
$2x < 5 + 5$
$2x < 10$
$x < 5$