2y< -12x+4 y<-6x+4

Answer 1

Break this problem up into two problems split at the inequality symbols:

Problem #1: 2y < -12x + 4y

1) subtract 4y from both sides to get: -2y < -12x

2) divide both sides by -2 (note that when you divide or multiply by a negative number in an inequality you MUST switch the sign): y > 6x

3) Graph this boundary line and shade the appropriate side (in this case above the line because y is greater than the line (6x):

Note that we use a dotted line because the line is NOT included in the solution since the symbol is greater than (not "greater than or equal to").

Problem 2: -12x + 4y < -6x + 4

1) Add 12x to both sides to get: 4y < 6x + 4

2) Divide both sides by 4 to get: y < 3/2x + 1

3) Graph the line on the same graph. The solution is the overlapping part:

Answer 2

Hi Syriah,

Since there are inequalities in this problem, the answer can be done by graphing each of these two lines (the lines will be dashed).

We can rewrite the first equation by dividing it by 2: y < -6x + 2. This is a line that passes through the point (0,2) and has a downward slope of -6.

The second equation passes through the point (0,4) and has a downward slope of -6.

Since the lines have the same slope, they are parallel and never intersect.

Since the first equation is below the second one, we can shade the area underneath it (the < symbol means that we shade below, a > symbol would mean we shade above).

The area we’ve shaded is the set of all points that are beneath both lines.

Please let me know if I can be more helpful, thanks!

Joe