solve and graph this inequality

Question

3 x + 2 y < 6

2 x - y > 2

Answer 1

Let's start by transforming them into linear inequalities. That means we solve for (isolate) y:

3x + 2y < 6

2y < -3x + 6

y < ^-3/₂x + 3

 

2x - y > 2

-y > -2x + 2

y < 2x - 2 (Remember, when we divide by a negative number, that means that we also have to flip the inequality)

 

Now you can graph these two lines (remember that inequalities mean that areas are going to be shaded, and as there isn't an "or equal to" part, the line will be dashed). Like a Venn diagram, the area that both parts share will be the shaded area.

 

 

Answer 2

In order to solve, we must graph. 

 

3 x + 2 y < 6               ineq1
2 x - y > 2                   ineq2

 

 

We need to get the inequalities in y = mx+b form.  But of course the equal sign is replaced with a comparison sign.

 

From ineq1.

 

2y < -3x + 6

 

  y < (-3/2)x + 3

 

 

From the ineq2.

 

-y > -2x + 2

 

 y > 2x - 2

 

 

Now we can graph the inequalities. 

 

If we graph y=(-3/2)x + 3 , then y < (-3/2)x + 3 is below the line.

If we graph y=2x - 2 , then y > 2x - 2 is above the line.

 

 

Shade the region that is below the line (-3/2)x + 3, but above the line  2x - 2.  The range of x values and range of y values in that shaded region is the solution.