Step-by-step explanation:
inequalities follow basically the same rules as equalities (ahem, equations). for creation and calculation.
you just indicate whole areas above or below given lines.
behind every inequality is a "normal" equation that defines the delimiter.
the question already tells us which variables to use.
x = number of hot dogs
y = number of peanuts (I guess, bags of peanuts)
he wants to buy at least 4 snacks.
hmmm.
what would you do, if the question asked us :
he wants to buy 4 snacks.
what did you learn from the previous questions ?
the equation would be
x + y = 4.
but now it asks us about "at least" 4 snacks. so every solution, 4 or more, is valid. not only 4.
so, the inequality is
x + y >= 4
and he has $20 to buy these snacks.
again, with equations we would have said
3x + 2y = 20
remember, a hot dog costs $3, a bag of peanuts costs $2. so, every single hot dog and every single bag of peanuts brings itself into the cost calculation with that amount.
x hot dogs cost $3x. y bags of peanuts cost $2y.
but here, we are now flexible. he can spend $20, but he does not have to fully exceed his budget. he can also spend less.
so, the inequality is
3x + 2y <= 20
together these inequalities now describe the situation that he cannot spend more than $20, but he can spend as little as he wants, as long as he gets at least 4 snacks.
all combinations of x and y values that satisfy these conditions are valid solutions.
the actual solution would be then more complex, as the real life scenario gives us more constraints :
0 <= x <= 6 (because with more than 6 hot dogs alone he would already bust his budget).
0 <= y <= 10 (after buying 10 bags of peanuts the $20 are gone).
that eliminates the negative value solutions that the basic 2 equations would allow.
