Our given inequality is 2x ≤ -2/3 (4x + 4) and our goal is to get x alone on one side of the inequality and not x on the other. We have that -2/3 out front being a pain in the butt fraction, so let's clear and multiply its denominator, 3. (It's also the lowest common denominator of 3 and 1 - the right side's invisible denominator)
(3) 2x ≤ (3) -2/3 (4x + 4) <-- clear fractions, multiply both sides by 3
6x ≤ -2 (4x + 4) <-- apply the multiplying, simplify on right side
6x ≤ -8x - 8 <--distribute the -2 and multiply it
14x ≤ -8 <---- add 8x to both sides
x ≤ -8 / 14 <--- divide both sides by 14
x ≤ -4 / 7 <--- divide the right side by 2 to simplify
Thus, x ≤ -4 / 7 makes this inequality true.