Given an inequality, what strategies can we use to determine where the boundary line is? Explain your strategies in detail. 4x+3y≥12

Step-by-step explanation:

The strategy to determine the boundary line is that we need to remove the inequality sign and replace it with and equal to sign and then sketch the equation of the function which is

to sketch the function we need the function's x-intercept which means the graphs crosses the x-axis at that specific point (x , 0) and y-intercept which means the graph crosses the y-axis at that specific point (0 , y).

Since both these points lie on line we can substitute it into the equation to find the x-y intercepts and hence sketch the line so here goes.

For x-intercept:

so the x-intercept is (3 , 0)

For y-intercept:

so the y-intercept is (0 , 4)

now we sketch these 2 points and draw a straight line joining both the points as shown in the image below.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

answer: can you give the

step-by-step explanation: