Question

Is the inequality always, sometimes or never true?

9(x+2) > 9(x-3)

answer is 2>3 and i said it's never true, right?

2. 6x-13 < 6(x-2)
answer is 6x-13 < 6x-12 my answer is sometimes

3. -6(2x-10) + 12x less than or equal to 180. im stuck.,

Answer 1

In order to understand if the inequalities are always, never or sometimes true, you need to perform the calculations:

A) 9(x+2) > 9(x-3)
9x + 18 > 9x - 27
the two 9x cancel out and you get:
+18 > -27
which is always true.

B) 6x-13 < 6(x-2)
6x - 13 < 6x - 12
the two 6x cancel out and you get:
- 13 < -12
which is always true

C) -6(2x-10) + 12x ≤ 180
-12x +60 +12x ≤ 180
-12x and +12x cancel out and you get:
60 ≤ 180
which is always true.

All three cases are always true.