Problem: Prove that the statements below are
equivalent
- y = 3x + b
- b = y - 3x
- x = (y - b) / 3
- Answers: Solve #2 for y. Add 3x to both sides: b + 3x
= y - 3x + 3x.
This becomes b + 3x = y.
Solve #3 for y. Multiply both sides by 3: 3x = 3(y -
b) / 3.
This becomes 3x = y - b. Now add b to both sides: 3x +
b = y - b + b
This becomes 3x + b = y
Now verify that they are equivalent by plugging in the
numbers
- y = 10, b = 4, x = 2.
- y = 3x + b becomes 10 = 3(2) + 4 = 6 + 4 = 10
OK
- b = y - 3x becomes 4 = 10 - 3(2) = 10 - 6 = 4
OK
- x = (y - b) / 3 becomes 2 = (10 - 4) / 3 = 6 / 3 =
2 OK
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Algebra
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Updated
8/16/99
By James
E. Heath