Pre calculus solving a compound linear inequality

Question

-4<7-3x<0 

please show work with steps! 

Answer 1

with compound inequalities, whenever you perform an operation you must do it to the left side, the middle and the right side. And if you multiply or divide by a negative number, then reverse all the inequalities

 

-4≤7-3x<0   subtract 7

 

-11 ≤ -3x < -7   divide by -3, and reverse the inequalities

 

11/3 ≥ x > 7/3

 

(7/3, 11/3] is the solution in interval notation

Answer 2

Jacie,

 

Handle this the same way as we did the last one except now we have to perform the same operation on the left, in the middle, and on the right (and remember what I said happens if we multiply or divide by negative numbers!).

 

Adding -7 all the way through:

 

-13 ≤ -3x < -7

 

Now multiply or divide by -1 (either works):

 

13 ≥ 3x > 7

 

Finally divide by 3

 

13/3 ≥ x > 7/3