Final answer:
The solution to the equation y = |x + 11| involves two cases: when x + 11 is greater than or equal to 0, and when it is less than 0. In the first case, the solution is y = x - 11, and in the second case, it is y = -x - 11.
Step-by-step explanation:
The equation y = |x + 11| represents an absolute value equation. To find the solution, we first consider two cases:
Case 1: When x + 11 ≥ 0
In this case, the equation becomes y = x + 11. To solve for y, we need to isolate x.
Step 1: Subtract 11 from both sides: y - 11 = x.
Step 2: Rearrange the equation to isolate y: y = x - 11.
Case 2: When x + 11 < 0
In this case, the equation becomes y = -(x + 11), since an absolute value of a negative number yields a positive result. To solve for y, we again isolate x.
Step 1: Distribute the negative sign: y = -x - 11.
Step 2: Rearrange the equation to isolate y: y = -x - 11.
Therefore, the solution to the equation y = |x + 11| is:
y = x - 11 (when x + 11 ≥ 0)
y = -x - 11 (when x + 11 < 0)