Question

What is the best way to classify each equation?
Column A Column B
1. 22 - 3x + 7x = 4(x + 5)

2.6(2x - 3) = 3(3x - 5)

3.6x - 14 = 2(3x - 7)

4.6x + 3 (x - 4) = 8(x - 3)

A.
identity
B.
contradiction
C.
neither

Answer 1

identity equations are always true no matter what you sub in for the variable...so basically, identity equations have infinite solutions.

contradiction equations have no solution.

so lets get to work....
22 - 3x + 7x = 4(x + 5) -- distribute through the parenthesis
22 - 3x + 7x = 4x + 20 -- simplify
22 + 4x = 4x + 20 -- subtract 4x from both sides
22 = 20 --- incorrect....no solution...contradictory

6(2x - 3) = 3(3x - 5) -- distribute through the parenthesis
12x - 18 = 9x - 15 -- subtract 9x from both sides
12x - 9x - 18 = -15 -- add 18 to both sides
12x - 9x = -15 + 18
3x = 3
x = 1.....this tells me that there is 1 solution....so it is neither

6x - 14 = 2(3x - 7) -- distribute through the parenthesis
6x - 14 = 6x - 14
0 = 0...correct.....this means there is infinite solutions.... identity

6x + 3(x - 4) = 8(x - 3) -- distribute through the parenthesis
6x + 3x - 12 = 8x - 24
9x - 12 = 8x - 24 --- subtract 8x from both sides
9x - 8x - 12 = -24 -- add 12 to both sides
9x - 8x = -24 + 12
x = - 12....this tells me there is 1 solution...so this one is neither also