Question

Write two equations without absolute value symbols that, in combination, are equivalent to |3x + 5| = 12. Solve each of these two equations.

Answer 1

To write two equations without absolute value symbols that are equivalent to |3x + 5| = 12, we need to consider both the positive and negative cases. The two equations are 3x + 5 = 12 and -3x - 5 = 12, with solutions x = 7/3 and x = -17/3, respectively.

Step-by-step explanation:

To write two equations without absolute value symbols that are equivalent to |3x + 5| = 12, we need to consider both the positive and negative cases.

1. If 3x + 5 is positive, then the equation 3x + 5 = 12 holds. Solving this equation gives x = 7/3.
2. If 3x + 5 is negative, then we need to consider the opposite sign. So the equation -(3x + 5) = 12 can be written as -3x - 5 = 12. Solving this equation gives x = -17/3.

Therefore, the two equations without absolute value symbols that are equivalent to |3x + 5| = 12 are 3x + 5 = 12 and -3x - 5 = 12. The solutions for these equations are x = 7/3 and x = -17/3, respectively.