( help ) Match the inequality on the left to the appropriate solution on the right. i accidentally selected those, so if you could tell me the answers to those aswell.

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.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,