add 5y to both sides of the inequality to get:
2x < 4 + 5y
subtract 4 from both sides of the inequality to get:
2x - 4 < 5y
divide both sides of the inequality by 5 to get:
2/5 * x - 4/5 < y
if a < b, then b > a, so your inequality becomes:
y > 2/5 * x - 4/5.
another way to solve this is shown below:
start with 2x - 5y < 4
subtract 2x from both sides of the inequality to get:
-5y < -2x + 4
multiply both sides of the inequality by -1 to get:
5y > 2x - 4
multiplying both sides of an inequality by a negative number reverses the inequalit6y.
divide both sides of the inequaity by 5 to get:
y > 2/5 * x - 4/5.
that's your inequality in slope intercept form.
your equation is y = 2/5 * x - 4/5.
any value of y greater than that satisfies your inequality.
for example:
when x = 5, y = 2/5 * x - 4/5 which becomes y = 2/5 * 5 - 4/5 which becomes y = 2 - 4/5 which becomes y = 1 and 1/5.
any value of y greater than 1 and 1/5 would satisfy the inequality.
any value of y less than or equal to 1 and 1/5 would not.
you would graph y = 2/5 * x - 4/5.
you would then shade the region above that line.
that's your region of feasibility.
any value of y in the shaded region satisfies the inequality.
note that the value of y has to have a corresponding value of x formed by the inequality.
for example, assume the value of y is 25.
the inequality states that 25 > 2/5 * x - 4/5.
add 4/5 to both sides of that inequality to get 25 + 4/5 > 2/5 * x.
solve for x to get 64.5 > x
any value of x less than 64.5 would satisfy the inequality.
for example, if x = 64, then 25 > 2/5 * 64 - 4/5 becomes 25 > 24.8 which satisfies the inequality.
as long as x is less than 64.5 the inequality would be saatisfied.
the equation of y = 2/5 * x - 4/5 can be graphed as shown below.
the area above the graph satisfies the inequality.
the area below or on the graph doesn't.
when you find a value of y above the line, you need to find the corresponding value of x.
the value of y is a coordinate point of (x,y) where the value of x is the corresponding value of x.
this is shown in the graph below for a value of y that is equal to 30.
that value of y = 30 will be greater than y = 2x - 4/5 for all values of x less than or equal to 77.
the graph looks like this.
the shaded graph looks like this:
in both graphs, you can see that any value of x less than 77 will satisfy the inequality.
let me know if you have any questions.
theo