20=∣y+21∣
To solve for y in the equation 20=|y+21|, we can first isolate the absolute value term by subtracting 21 from both sides:
20 - 21 = |y+21| - 21,
-1 = |y+21| - 21.
Next, we can separate the absolute value into two cases, one for when the expression inside the absolute value is positive and one for when it is negative.
Case 1: y+21 > 0
In this case, the expression inside the absolute value becomes y+21, so we have:
-1 = y+21 - 21,
-1 = y.
Therefore, in this case, y = -1.
Case 2: y+21 < 0
In this case, the expression inside the absolute value becomes -(y+21), so we have:
-1 = -(y+21) - 21.
To simplify this equation, we can distribute the negative sign:
-1 = -y - 21 - 21,
-1 = -y - 42.
Next, we want to isolate the variable y by adding y and 42 to both sides:
-1 + y + 42 = -y - 42 + y + 42,
41 + y = 0.
Finally, we can subtract 41 from both sides to find y:
y = 0 - 41,
y = -41.
Therefore, in this case, y = -41.
In summary, the equation 20=|y+21| has two solutions: y = -1 and y = -41.