|z - 1| = 7z - 13 solve this equation and check for extraneous solutions

Given:  |z-1| = 7z - 13

Due to the absolute value function, this equation yields two separate equations:

+(z-1) = 7z - 13, and

-(z-1) = 7z - 13.

Simplifying the first, we get z - 1 = 7z - 13, or

                                               -1 + 13 = 7z - z, or 12 = 6 z.  Then z = 2.

Doing the same to the 2nd equation:   -z + 1 = 7z - 13, or 14 = 8z, or z = 7/4.

We must check both results by subst. into  |z-1| = 7z - 13:

If z = 2, we get 2 - 1 = 14 - 13, or 1 = 1.  Thus, z = 2 is a solution.

If z = 7/4, we get 3/4 = 7(7/4) - 13, or   3/4 = 49/4 - 52.  This is clearly false.

The (single) solution is thus z = 2

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.