Final answer:
The word problem translates into the inequality expression ¼(t + 9) ≤ 9, which simplifies to t ≤ 27 when the fraction is cleared and both sides are simplified.
Step-by-step explanation:
To translate the word problem 'One-fourth multiplied by the sum of t and 9 is at most 9' into an inequality expression, we first need to formulate the expression that represents 'one-fourth multiplied by the sum of t and 9'. This is written algebraically as ¼(t + 9). The phrase 'is at most 9' indicates that this expression should be less than or equal to 9, which gives us the inequality:
¼(t + 9) ≤ 9
To make this easier to work with, you might want to clear the fraction by multiplying both sides of the inequality by 4, which would result in:
t + 9 ≤ 36
And then simplifying further by subtracting 9 from both sides gives us:
t ≤ 27
This demonstrates that t must be less than or equal to 27.