Final answer:
Solving the linear inequality 4A + 2B ≤ 4 involves graphing the boundary line 4A + 2B = 4, determining the intercepts, and testing a point to find the solution region. The area including and below the line represents the set of solutions for (A, B).
Step-by-step explanation:
The student is dealing with a linear inequality in two variables, which is a topic in algebra. The inequality to solve is 4A + 2B ≤ 4. To find the solutions that satisfy this inequality, one can graph the equation 4A + 2B = 4, which represents the boundary of the inequality on a coordinate plane with A on the horizontal axis and B on the vertical axis.
The boundary line can be found by determining where the line intercepts the A-axis (when B = 0) and the B-axis (when A = 0). If B = 0, then A = 1. If A = 0, then B = 2. Plotting these two points and drawing a line through them gives us the boundary line.
To determine the solution region, we can test a point not on the line, such as (0,0), in the inequality 4A + 2B ≤ 4. Since 0 satisfies the inequality, the area including (0,0) on the graph will be the solution set. Thus, the region below and on the line represents all pairs of (A, B) that are solutions to the inequality.