The best answer for the inequality using both the graphical and algebraic approach is B. x > 2 Graph A.
How to solve inequality?
Solve the inequality 5 - x < 2(x - 3) + 5 algebraically:
5 - x < 2x - 6 + 5
Combine like terms:
5 - x < 2x - 1
Add x to both sides:
5 < 3x - 1
Add 1 to both sides:
6 < 3x
Divide by 3 (note that dividing by a positive number does not change the direction of the inequality):
2 < x
Now, analyze the graphs:
Graph A:
Line 1: y = -x + 5, passing through (0, 5) and (5, 0).
Line 2: y = x + 1, passing through (-2, -4) and (2, 3).
The intersection point is (2, 3).
Graph B:
Line 1: y = -3x, passing through (0, 0) and (2, -6).
Line 2: y = -2x - 8, passing through (0, -8) and (2, -6).
The intersection point is (2, -6).
Now, to answer the questions:
a. x > 2 Graph A: False
The correct solution is x > 2 based on the algebraic solution.
b. x > 2 Graph A: True
This matches the solution x > 2 from the algebraic approach.
c. x > 2 Graph B: False
The correct solution is x > 2 based on the algebraic solution.
d. x > 2 Graph B: False
The correct solution is x > 2 based on the algebraic solution.
Therefore, the best answer is B. x > 2 Graph A.
Complete question:
Solve the following inequality using both the graphical and algebraic approach: 5 minus x less-than 2 (x minus 3) + 5 Graph A On a coordinate plane, a line goes through (0, 5) and (5, 0). Another line goes through (negative 2, negative 4) and (2, 3). The lines intersect at (2, 3). Graph B On a coordinate plane, a line goes through (0, 0) and (2, negative 6). Another line goes through (0, negative 8) and (2, negative 6). a. x less-than 2 Graph A b. x greater-than 2 Graph A c. x less-than 2 Graph B d. x greater-than 2 Graph B Please select the best answer from the choices provided A B C D