Solve the compound inequality 5x+7 < 13 or -4x+3 > 11. Graph the solution.

The correct answer is: the final inequality is x < 6/5.

Solving the first inequality for x

5x + 7 < 13

5x < 13 - 7

5x < 6
x < 
Solving the second inequality for x
-4x + 3 > 11

-4x > 11 - 3
-4x > 8
Dividing -4 both sides

x < 

x < -2
So, the final result is x <  or x < -2
Plotting the graph

 
Final Answer:
 Hence, the final inequality is x < .

A Compound inequality is a connection between two inequality statements by the words "or" or "and." The conjunction "and" denotes the simultaneous truth of both statements in a compound sentence. It is the point where the solution sets for the various statements cross over or intersect. The conjunction "or" denotes that the entire compound sentence is true as long as either of the two statements is true — the union or combination of the solution sets for each particular statement.
Let's see x: 2 x + 7 < –11 or –3 x – 2 < 13. Solve each inequality on its own. Combine the solutions, i.e., determine the union of the solution sets for each inequality phrase since the connecting word is "or." Both x < –9 and x > -5 denote all the numbers on the left of those two particular values. Written as follows is the solution set:
{ x| x < -9 or x > -5}