Solution for Problem 1.3.2

Solve for x3x2 + x = 2

Solve

Step

3x2 + x 2 =  0 Factor, if possible. 
(3x 2)(x + 1) = 0 You must equation equal to 0 first.
3x 2 = 0 or x + 1 = 0 Solve each linear equation separately
3x 2 = 0 gives 3x =2 Zero Property of Multiplication
x = 2/3 If ab = 0 then a = 0 or b = 0
x + 1 = 0 gives x = -1
{-1, 2/3} Solution Set Notation

Solve

If x = -1, then
3(-1)2 + (-1) = 2  
    3 1 = 2 

If x = 2/3, then
3(2/3)2 + (2/3) = 2  
    3(4/9) + 2/3 = 2 
4/3 + 2/3 = 2
6/3 = 2