Consider the equation x + 4 = 3x + 2.
a. show that adding x + 2 to both sides of the equation does not change the solution set.
b. show that multiplying both sides of the equation by x + 2 adds a second solution of x = -2 to the solution
set.

Step-by-step explanation:

Given

(a)x+4=3x+2

x=1

adding x+2 both sides we get

x+4+x+2=3x+2+x+2

2x+6=4x+4

2x=2

x=1

so adding x+2 does not change solution of equation

(b)

thus x=-2 adds in the solution of the Equation

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: