Solve the absolute value equation. $$ |b|=12 $$

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UpStudy AI · Accepted Answer

To solve the absolute value equation:

$$
|b| = 12
$$

**Understanding Absolute Value:**

The absolute value of a number represents its distance from zero on the number line, regardless of direction. Therefore, the equation $$ |b| = 12 $$ means that $$ b $$ is **12 units away** from zero. This leads to two possible scenarios:

1. **Positive Scenario:**
   $$
   b = 12
   $$
   
2. **Negative Scenario:**
   $$
   b = -12
   $$

**Solution:**

$$
b = 12 \quad \text{or} \quad b = -12
$$

**Conclusion:**

The equation $$ |b| = 12 $$ has two solutions:
$$
b = 12 \quad \text{and} \quad b = -12
$$
The solutions are $$ b = 12 $$ and $$ b = -12 $$.

Solve the absolute value equation.

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