Question

Which of the answer choices below has the same solution set as the inequality y minus 8 less-than-or-equal-to negative 2?
y minus 8 + 8 greater-than-or-equal-to negative 2 + 8
y minus 8 + 8 less-than negative 2 + 8
y minus 8 + 2 less-than-or-equal-to negative 2 + 8
y minus 8 + 2 less-than-or-equal-to negative 2 + 2

Answer 1

Start with y − 8 ≤ −2. Add 6 to both sides (or simplify directly):

y − 8 ≤ −2
y − 6 ≤ 0 (equivalently y ≤ 6)

Check choices:
1) gives y ≥ 6 (wrong direction),
2) gives y < 6 (strict, wrong),
3) gives y ≤ 12 (wrong),
4) gives y − 6 ≤ 0, i.e. y ≤ 6 (same).

So the fourth choice is correct.