Solve the absolute value equation. $$ |5 n+9|+12=5 $$ Select the correct choice below and. if necessarv. fill

Question

UpStudy AI · Accepted Answer

To solve the absolute value equation:

$$
|5n + 9| + 12 = 5
$$

**Step 1: Isolate the Absolute Value**

Subtract 12 from both sides of the equation:

$$
|5n + 9| = 5 - 12
$$
$$
|5n + 9| = -7
$$

**Step 2: Analyze the Absolute Value**

The absolute value of any real number is always **non-negative** (i.e., it is either positive or zero). Therefore, an absolute value cannot be equal to a negative number.

$$
|5n + 9| = -7 \quad \text{(This is impossible)}
$$

**Conclusion:**

There is **no solution** to the equation because the absolute value cannot be negative.

**Answer:**  
**No solution.**
There is no solution to the equation.

Solve the absolute value equation.

Select the correct choice below and. if necessarv. fill

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Solve the absolute value equation. Select the correct choice below and. if necessarv. fill