Let's say she does the absolute minimum and buys 4 bags
Each bag has 7 servings, so there are 7*4 = 28 servings total.
I'm assuming each of the 30 guests gets one serving only. If so, then there wouldn't be enough food to go around (30-28 = 2 people are left out).
This means she cannot round x = 4.3 to x = 4. Instead, she must round up to get x = 5 as the lowest x value possible.
7x = 7*5 = 35 servings clears the hurdle.
So in short, x = 4 does not work in
but x = 5 does work in
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Alternatively, you could plug in x = 4 into
to get
which is not a true statement. So x = 4 is not a solution to
However, x = 5 is a solution since
is a true statement.