28) Solve. List all answers in interval notation. a) $$ -4 x^{2}

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28) Solve. List all answers in interval notation. a) $$ -4 x^{2}<8 $$

UpStudy AI · Accepted Answer

To solve the inequality:

$$
-4x^{2} < 8
$$

**Step 1: Isolate $$ x^{2} $$**

Divide both sides of the inequality by **-4**. **Remember:** Dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.

$$
x^{2} > \frac{8}{-4}
$$

$$
x^{2} > -2
$$

**Step 2: Analyze the Inequality**

The expression $$ x^{2} $$ represents a squared term, which is always **non-negative** (i.e., $$ x^{2} \geq 0 $$) for all real numbers $$ x $$.

Since $$ x^{2} $$ is always greater than or equal to 0, and 0 is already greater than -2, the inequality:

$$
x^{2} > -2
$$

is **always true** for all real numbers $$ x $$.

**Conclusion:**

All real numbers satisfy the inequality. Therefore, the solution in interval notation is:

$$
(-\infty, \infty)
$$

**Answer:**  
All real numbers satisfy the inequality.  
Interval notation: $$(-∞, ∞)$$
All real numbers satisfy the inequality. Interval notation: $$(-∞, ∞)$$

28) Solve. List all answers in interval notation. a) \( -4 x^{2}<8 \)

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