Solve the absolute value equation. $$ |y|+3=-3 $$

Question

UpStudy AI · Accepted Answer

To solve the absolute value equation:

$$
|y| + 3 = -3
$$

**Step 1: Isolate the Absolute Value**

Subtract 3 from both sides of the equation to isolate the absolute value expression:

$$
|y| + 3 - 3 = -3 - 3 \
|y| = -6
$$

**Step 2: Analyze the Absolute Value**

The absolute value of a number, $$|y|$$, represents its distance from zero on the number line and is always **non-negative** (i.e., $$|y| \geq 0$$).

However, in this equation, we've arrived at:

$$
|y| = -6
$$

This states that the absolute value of $$y$$ is equal to $$-6$$, which is **impossible** because absolute values cannot be negative.

**Conclusion:**

There is **no solution** to the equation $$|y| + 3 = -3$$.
There is no solution to the equation $$|y| + 3 = -3$$.

Solve the absolute value equation.