SOLUTION: [ 4-5x] -1 = 33 I understand this topic on my HW and get at least an 85% but at test time i almost always fail within the 30% range. 1 more question/example [ 7k + 2 ]+3 <12

Question 140184: [ 4-5x] -1 = 33
I understand this topic on my HW and get at least an 85% but at test time i almost always fail within the 30% range.
1 more question/example
[ 7k + 2 ]+3 <12
for #1 what i did was
I subtracted 4 from both 4 and 33 which gave me [-5x] -1 =33
then i took away the absolute value bars and made it an equation -5x-1=29
for my answer my teacher said i got the first 1/2 right by getting -6 but for the positive number (i put +6) she said i did it wrong.
for the second one i was the only one who missed it so please tell me if there's a trick
i re-wrote the absolute value and subtracted 3 from all sides then came up with 7k+2 my answer was k<=1 >-3 the less than sign with an equal is less than or equal to. She said i missed the whole thing.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
absolute value is the LAST operation; because for abs(x)=y, both +y AND -y satisfy the equation

abs(4-5x)-1=33 __ adding 1 __ abs(4-5x)=34

now absolute value __ 4-5x=34 __ -5x=30 __ x=-6
__ AND __ 4-5x=-34 __ -5x=-30 __ x=6

abs(7k+2)+3<12 __ subtracting 3 __ abs(7k+2)<9

absolute value __ 7k+2<9 __ 7k<7 __ k<1
__ AND __ 7k+2>-9 __ 7k>-11 __ k>-11/7

when you multiply the < value by -1, remember to change the direction to >
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