Question 108980
{{{abs(5k+2)-3<=4}}} Start with the given inequality



{{{abs(5k+2)<=7}}} Add 3 to both sides.



Break up the absolute value (remember, if you have {{{abs(x)<= a}}}, then {{{x >= -a}}} and {{{x <= a}}})


{{{5k+2 >= -7}}} and {{{5k+2 <= 7}}} Break up the absolute value inequality using the given rule



{{{-7 <= 5k+2 <= 7}}} Combine the two inequalities to get a compound inequality




{{{-9 <= 5k <= 5}}} Subtract 2 from  all sides



{{{-9/5 <= k <= 1}}}  Divide all sides by 5 to isolate k




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Answer:


So our answer is


{{{-9/5 <= k <= 1}}}




which looks like this in interval notation



*[Tex \LARGE \left[\frac{-9}{5},1\right]]


note: since the inequality was less than or <b>equal</b> to, that means the end points are included. So that is why brackets are used instead of parenthesis.