Final answer:
Sue cannot buy any gas because she cannot afford the rental fee and the cost of gas within her budget.
Step-by-step explanation:
To write the story problem as an inequality expression, we need to define variables for the quantities involved. Let's say x represents the number of gallons of gas Sue can buy. The total cost, including the rental fee, will be $50 + $3x. Based on the information given, Sue can spend at most $38. To write this as an inequality, we have:
$50 + $3x ≤ $38
To solve this inequality and find the maximum number of gallons Sue can buy, we need to isolate x. We can start by subtracting $50 from both sides:
$3x ≤ $38 - $50
$3x ≤ - $12
Next, divide both sides by $3 to solve for x:
x ≤ - $12 ÷ $3
x ≤ - 4
This means that Sue can buy at most -4 gallons of gas, which is not possible. So, in this situation, Sue cannot buy any gas.