These sheets include negative coefficients, which is where inequalities stop behaving like equations: -2x > 8 gives x < -4, not x > -4. Dividing both sides by a negative reverses the relation.
It is the one rule in this topic students reliably get wrong, and the only way to practise it is on problems that contain it. Roughly half the coefficients on each sheet are negative, so a student cannot get through without meeting the case.
Because multiplying or dividing by a negative reverses the order of the number line. 2 is less than 6, but -2 is greater than -6. The same happens to an inequality when both sides are divided by a negative.
No. Only multiplying or dividing by a negative reverses the relation. Adding and subtracting leave it alone, which is what makes the rule easy to over-apply.
Pick a number that satisfies your answer and put it back into the original. If you say x < -4, try -5: -2 × -5 is 10, which is greater than 8, so it works.
Seventh grade, after negative numbers and one-variable inequalities are both familiar on their own.