Question

Which conjunction or disjunction is equivalent to the open sentence |a – 8| ≤ 3.

A.
a – 8 ≤ 3 and a – 8 ≥ –3

B.
a – 8 ≥ 3 and a – 8 ≤ –3

C.
a – 8 ≤ 3 or a – 8 ≥ –3

D.
a – 8 ≥ 3 or a – 8 ≤ –3

Answer 1

|a – 8| ≤ 3

if (a-8) is positive, then the | | don't do anything, and we can write just
a-8 ≤ 3
so the answer should have at least this part.

Answer 2

so the answer is either A or C

Answer 3

thanks man :D Ima go A

Answer 4

if (a-8) is negative, then if we multiply by -1, it will be positive so we can drop the | |
-(a-8) ≤ 3

none of the choices look like that so we have to rearrange it.

Answer 5

if we have
-(a-8) ≤ 3

it's tricky to multiply or divide both sides by a *negative* number. But it's always safe to add or subtract the same thing from both sides.

so add (a-8) to both sides
(a-8) - (a-8) ≤ 3 + (a-8)
or
0 ≤ a-8 + 3
add -3 to both sides
-3 ≤ a-8
or
a-8 ≥ -3