Question

Can someone tell me if I am doing this the correct way? I have to figure out if it is always, sometimes, or never true.
2(8x-4)-2x (is less than or equal to) 14x+12
I know you distribute making it:
16x-8-2x (is less than or equal to) 14x+12 then, I got
14x-8 (is less than or equal to) 14x+12
What is the next step? Do I subtract 14x from both sides and get -8 is less than or equal to 12?

Answer 1

2(8x - 4)- 2x <= 14x + 12
16x - 8 - 2x <= 14x + 12
14x - 8 <= 14x + 12 (subtract 14x from both sides)
14x - 14x - 8 <= 12 (now add 8 to both sides)
0 - 8 + 8 <= 12 + 8
0 <= 20

test it...
14x - 8 <= 14x + 12 (test number 5)
14(5) - 8 <= 14(5) + 12
70 - 8 <= 70 + 2
62 <= 72 (true)

use -5 as your test number
14x - 8 <= 14x + 12
14(-5) - 8 <= 14(-5) + 12
-70 - 8 <= -70 + 12
-78 <= - 58 (true)

It is ALWAYS TRUE