Solve for all values of bb in simplest form.open vertical bar, b, minus, 4, close vertical bar, equals, 38∣b−4∣=38
Question
Solve for all values of in simplest form.
Given the equation:
You need to find the values of .
Solution
The absolute value equation |b - 4| = 38 can be solved by setting up two separate equations, because the absolute value of a number can be either positive or negative.
- b - 4 = 38
- -(b - 4) = 38
Solving the first equation: b - 4 = 38 b = 38 + 4 b = 42
Solving the second equation: -(b - 4) = 38 b - 4 = -38 b = -38 + 4 b = -34
So, the solutions for the equation |b - 4| = 38 are b = 42 and b = -34.
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