Answer:
First inequality --- No solution *third option in the list)
Second inequality ---- First (top) plot option in the list.
Third inequality ----- Second plot option in the list.
Fourth inequality ----- Last (bottom) plot option in the list.
Step-by-step explanation:
We solve for "x" in each inequality to find the appropriate graph:
First set:
3 x +2 < 11 then 3 x < 9 therefore x < 3
and
(1/2) x - 2 > 2 then (1/2) x > 4 therefore x > 8
Since this combination requires x values to be smaller than 3 and larger than 8, that is an impossible, so there is no solution for this (empty set of solutions). So connect with the third option "No solution."
Second set:
4 < 2 x -2 then 6 < 2 x therefore 3 < x
and
2 x - 2 < 14 then 2 x < 16 therefore x < 8
so this is the set of x values between 3 and 8 on the number line (top graph - first option)
Third set:
3 x + 4 < 13 then 3 x < 9 therefore x < 3
or
x - 7 > 1 then x > 8
So, this is a set composed of the union of the set of numbers larger than 8, and the set of numbers smaller than 3. Connect to the second drawing in the list.
Fourth set:
- 3 x + 2 < -7 then 2 + 7 < 3 x , that is 9 < 3 x therefore 3 < x
and
x - 4 > 4 then x > 8
So this set (x-values larger than 3 and also larger than 8, is the set of all numbers larger than 8. Corresponds to the last (bottom) drawing in the list.
