Answer:
- See all four answers with their explanation below and the graph attached.
- The green arrow on the number line is the solution of the inequality.
Step-by-step explanation:
a). Description of what Brian did wrong.
Brian did not solve the inequality correctly. It seems he made several wrong steps:
- He added up 2 and 3 to get 5, which is wrong because 2 and 3 are in opposite sides of the inequality
- He use the symbol <, which is wrong because there is a negative sing in front of the varialbe (x) which changes the symbol to >.
b). Your work solving the inequality:
- Subtract 2 from both sides:
- x < 3 - 2
-x < 1
- Muliply both sides by - 1, which changes the symbol < to >:
x > - 1
Then the solution of the inequality is all the real numbers greater than - 1.
c). The correct solution graphed on a number line
- Since the number - 1 is not included in the solution set of the inequality you must use an oper circle around the number - 1 on the number line.
- Since the solution set is all the numbers greater than - 1 you draw an arrow pointing to the right of the number - 1 on the number line.
- See the correct graph in the diagram attached. The green line on the number line is the solution to the inequality.
d). The correct solution in set notation.
Three valid forms indicating the solution in set notation are:
- {x: > - 1}, which is read x such that x is greater than - 1
- x , which is read x such that x is greater than - 1
- x ∈ R , which is read, x belonging to real numbers, such that x is greater than - 1.
Both the colon (:) and the straight bar (|) mean "such that".