I need help with some <span title="Inequality/Regular/Absolute">Inequality/Regular/Absolu...</span> value equations. I always seem to get the wrong answers...?

Question

Regular Equation:

1) a(bx+2) = cx-12

2) 3p - 1 = 5(p-1) - 2(7-2p)

Absolute Value:

3) 4I4-3xI = 4x + 6

Inequality:

4) 12x-3x+11 > 4x - (17-9x)

Answer 1

1)you have ab x + 2a = cx - 12---&gt; ab x - cx = -12 -2a---&gt; (ab-c)x = -12-2a---&gt; x = [-12-2a] /[ab-c]

2) you have 3p-1 = 5p-5 -14 + 2p---&gt; -1 + 19 = 7p - 3p---&gt; 18 = 4p---&gt; 9/2 = p

3) you have | 4 - 3x| = x +3/2 ≥ 0---&gt; x has to be ≥ - 3/2 in the answer....|4-3x| = 4 - 3x if 4/3 ≥ x and the problem is now 4-3x = x + 3/2 or 5/2 = 4x or x = 5 / 8 { which is in [-3/2, 4/3] }....| 4 - 3x| = -[4-3x] if x ≥ 4/3 and the problem is then -4 +3x = 4x + 6 or x = -10, {which is not in [4/3,∞)}....so answer is x = 5/8

4) you have 9x + 11 &gt; 13 x -17----&gt; 28 &gt; 4x---&gt; 7 &gt; x