1.  Graph the associated quadratic function.
  x² - 7x + 10 = y   which is   y = x² - 7x + 10

2. , #6 Analyze, Graph #1 Zero
to find the zeros of the parabola, at (2,0) and (5,0),

3. In solving the inequality, we need the quadratic expression to be less than zero. This will be satisfied where the graph is below the x-axis.

The graph shows the quadratic to be below the
x-axis between x = 2 and x = 5.

Solution in Interval Notation: (2,5)

or 2 < x < 5

We have two choices for this solution.
We can subtract 8 from both sides, creating a zero on one side, and follow the procedure from example #1. That would be fine and dandy!

But, we are going to look at solving this problem in its current form.

1.  Graph each side of the inequality as two functions:  y = 3x² + 10x   and   y = 8

This time we will be looking for the sections of the parabola that will be greater than (above) the line y = 8.

2. , #6 Analyze, Graph #4 Intersection
to find where the line y = 8 intersects with the parabola. (-4,8) and (-.667,8)

3. In solving the inequality, we need the quadratic expression to be greater than 8. This will be satisfied where the quadratic graph is above the line y = 8.

The graph shows the solution to be to the left of
x = -4 or to the right of x = 5.

Solution: x < -4 or x > 0.667

Solution: