Question

When setting up an absolute value problem, the positive equation is exactly like the problem with the absolute value bars off, and the negative equation; you must flip the sign and make the right-hand side negative.

(a) True
(b) False

Answer 1

The statement is true. When dealing with absolute value equations, you create one equation identical to the original without the absolute value for the positive scenario and another that takes into account the negative possibility by flipping the sign and changing the right-hand side to its negative equivalent.

Step-by-step explanation:

The question posed is whether when setting up an absolute value equation, you keep the equation exactly the same when removing the absolute value bars for the positive case flip the sign, and make the right-hand side negative for the negative case. The answer to this question is true.

When you have an equation with an absolute value, you set up two separate equations: one that is the same as the original without the absolute value signs for the positive case, and another where you take into account that the inside of the absolute value could be negative by flipping the sign of the inequality or equation and making the right-hand side negative (if it's a constant).

For example:

|Ax + B| = C

This would yield two cases:

1. Ax + B = C
2. -(Ax + B) = C, which simplifies to Ax + B = -C or Ax = -C - B

Where A, B, and C are constants.