43=∣y−8∣
The equation 43 = |y - 8| can be solved by considering the two possible cases when the absolute value is positive or negative.
1) When |y - 8| is positive:
In this case, we can simply remove the absolute value and set y - 8 equal to 43:
y - 8 = 43
Adding 8 to both sides gives us:
y = 51
2) When |y - 8| is negative:
In this case, we need to change the sign of the absolute value expression and set it equal to 43 (making sure the expression inside the absolute value becomes negative):
-(y - 8) = 43
Expanding the expression by distributing the negative sign gives us:
-y + 8 = 43
Subtracting 8 from both sides gives us:
-y = 35
Multiplying both sides by -1 to solve for y gives us:
y = -35
Therefore, the two possible solutions for the equation 43 = |y - 8| are y = 51 and y = -35.