please help.

[8dltndus]

Hi,i'm in 7th grade and i tried 5 different ways to solve this problem but i just can't get the answer.
So, the problem is:

Solve and graph each compound inequality. (I don't have to graph it)
2c-10<5-3c<7c

what i first did was to divide 2c to every problem and then somehow i got
-9<5-c<5c
then i tried to subtract every problem by 5 which i think that's where i made a mistake.
Finally I got -14<-c<5c
and now i'm trying to divide all that by 5c which doesn't make sense to me. -_-;;
What's more confusing is that the answer on the answer key says it's 0.5<c<3
What am I supposed to do?

P.S.i know how to do simple inequalities but not the compound ones.

 

[Deleted member 4993]

Hi,i'm in 7th grade and i tried 5 different ways to solve this problem but i just can't get the answer.
So, the problem is:

Solve and graph each compound inequality. (I don't have to graph it)
2c-10<5-3c<7c

what i first did was to divide 2c to every problem and then somehow i got
-9<5-c<5c

Above does not make sense.

Are you trying to subtract 2c from each part?

Then you should get:

-10 < 5 - 5c < 5c

That would be correct step. Now you can divide each part by 5 and continue...


then i tried to subtract every problem by 5 which i think that's where i made a mistake.
Finally I got -14<-c<5c
and now i'm trying to divide all that by 5c which doesn't make sense to me. -_-;;
What's more confusing is that the answer on the answer key says it's 0.5<c<3
What am I supposed to do?

P.S.i know how to do simple inequalities but not the compound ones.

.

 

[soroban]

Hello, 8dltndus!

Solve and graph each compound inequality. (I don't have to graph it)

. . \(\displaystyle 2c-10\:<\:5-3c\:<\:7c\)

You have two inequalties . . . Solve them separately.

. . \(\displaystyle \begin{array}{ccccc}2c - 10 \:<\:5-3c &\Rightarrow& 5c \:<\:15 &\Rightarrow& c \:<\:3 \\ \\ 5-3c \:<\:7c &\Rightarrow& -10c \:<\:-5 &\Rightarrow& c \:>\:\frac{1}{2} \end{array}\)


Therefore: .\(\displaystyle \frac{1}{2} \:<\:c \:<\:3\)

. . \(\displaystyle -\!-\!-\!+ \!-\!- \circ\!=\!=\!\bullet\!=\!=\!=\!=\!=\! \bullet \!=\!=\!=\!=\!=\! \circ ---\)
. . . . . . .\(\displaystyle 0\) . . . . . . . \(\displaystyle 1\) . . . . . .\(\displaystyle 2\)nxx . . . \(\displaystyle 3\)