Question

-7<4k+5<33
what is the solution set of the inequality

Answer 1

you can answer this question in 2 way the first: break it down to 2 equations the first -7<4k+5 and the secon 4k+5<33. the second way is to do it together like so

Answer 2

\[-7<4k+5<33 /-5 \rightarrow -12<4k<28 /:4 \rightarrow -3<k<7\]

Answer 3

as you can see I'm doing the same action on all parts of the Inequality as long as I'm not dividing by 0 or by any negative number every thing is fine. if I'm dividing by any negative number I need to change the sign (ex: 1<-x --> -1>x)

Answer 4

so how would i get the answer

Answer 5

look at the post above: I wrote there the way and the solution the answer is -3<k<7 or in another form of writing (-3,7)

Answer 6

at first we subtract 5 from all the parts of the inequality that way we get
\[-7-5<4k+5-5<33-5\]

Answer 7

so we get \[-12<4k<28\] so far so good?

Answer 8

yes

Answer 9

now we divide every thing by 4
\[\frac{ -12 }{ 4 }<\frac{ 4k }{ 4 }<\frac{ 28 }{ 4 }\]
so we get the final answer:
\[-3<k<7\]

Answer 10

is it clearer now?

Answer 11

yes