David Gwyn J. answered • 10/24/20
Highly Experienced Tutor (Oxbridge graduate and former tech CEO)
3/8x< -6 or 5x > 2
Let's get x on its own in both:
x < 8/3 (-6) => x < -16
5x > 2 => x > 2/5
That's two separate ranges of x (less than -16 and more than 2/5).
To picture the size of the ranges:
x < -16 is same as -infinity < x < -16
and x > 2/5 is same as 2/5 < x < infinity
You can show this in two forms:
(a) an x/y graph, draw vertical lines at x = 2/5 and x = -16. shade the left of x = -16, and the right of x = 2/5. ie empty area between two lines.
(b) draw a number line (straight line) with numbers from, say, -20 to +6.
mark -16 with a small circle, NOT filled in (means not included, less than). And draw a heavy line from circle going left (negative). Mark 2/5 with small circle (again NOT filled in), and draw heavy line from circle going right (positive).
