Question

Solve for all values of y in simplest form.
43=∣y−8∣

Answer 1

The equation 43 = |y - 8| has two solutions, y = 51 and y = -35, which are obtained by considering both cases of the absolute value.

Step-by-step explanation:

To solve for all values of y in the equation 43 = |y - 8|, we must consider both cases of the absolute value function:

1. y - 8 = 43
2. y - 8 = -43

For case (1), adding 8 to both sides gives us:

y = 43 + 8

y = 51

For case (2), adding 8 to both sides gives us:

y = -43 + 8

y = -35

Therefore, the solution contains two values for y:

• y = 51
• y = -35