The equation you've provided is:

$|x| + y = 4$

To solve this equation, you would typically need to express it in terms of either $x$ or $y$. Since it involves an absolute value, the solution can differ depending on the sign of $x$.

Case 1: When $x \geq 0$

If $x$ is positive or zero, $|x| = x$. The equation becomes:

$x + y = 4$

This can be rearranged to solve for $y$:

$y = 4 - x$

Case 2: When $x < 0$

If $x$ is negative, $|x| = -x$. The equation becomes:

$-x + y = 4$

This can be rearranged to solve for $y$:

$y = 4 + x$

Final Answer

• For $x \geq 0$, the equation is $y = 4 - x$.
• For $x < 0$, the equation is $y = 4 + x$.

This represents two linear equations, with the solution depending on whether $x$ is non-negative or negative.

Would you like a graph of this, or any further clarification?

---

Here are five related questions you might find interesting:

1. What is the graph of the equation $|x| + y = 4$?
2. How does the behavior of $y = 4 - |x|$ compare to the linear equation without the absolute value?
3. What happens to the equation if we add or subtract a constant from $y$?
4. How do you solve an equation involving absolute values for both $x$ and $y$?
5. What would the solution be if the equation were $|x| - y = 4$?

Tip: Always consider both cases when dealing with absolute value equations, as they often split the equation into two different forms depending on the sign of the variable inside the absolute value.