Solve: |y - 5| + 6 = 16

To give multiple answers, list your answers separated by a comma.

y =

The solutions for the equation |y - 5| + 6 = 16 are y = 15 and y = -5. This is determined by isolating the absolute value and solving two separate equations derived from the definition of absolute value.
;

Answered by Anonymous | 2025-07-04

To solve the equation ∣ y − 5∣ + 6 = 16 , you first need to isolate the absolute value term. Here’s how you can solve it step-by-step:

Subtract 6 from both sides of the equation :
∣ y − 5∣ + 6 − 6 = 16 − 6
∣ y − 5∣ = 10

Solve for the expression inside the absolute value :
The absolute value equation ∣ y − 5∣ = 10 means the expression inside the absolute value can be either 10 or -10.
So, we set up two equations:
a. y − 5 = 10
b. y − 5 = − 10

Solve each equation :
a. For y − 5 = 10 :
y = 10 + 5
y = 15
b. For y − 5 = − 10 :
y = − 10 + 5
y = − 5

List the solutions :
Therefore, the solutions to the equation ∣ y − 5∣ + 6 = 16 are y = 15 and y = − 5 .


In summary, the values of y that satisfy the original equation are 15 and − 5 .

Answered by LiamAlexanderSmith | 2025-07-06