Which equation expresses a in terms of x given a = 8/(x+9)?

• A. a = 8/(x + 9)
• B. a = (x + 9)/8
• C. a = x/(8 + 9)
• D. a = 8x + 9

Answer: (A)

The main idea is that a is already given directly as a function of x. Expressing a in terms of x means keep the same relationship: a equals 8 divided by (x plus 9). So the expression in terms of x is a = 8/(x+9). Remember that x cannot be -9, since that would make the denominator zero.

The other forms change the relationship: swapping numerator and denominator would give a reciprocal, leading to a different value; using x/(8+9) simplifies to a = x/17, which ignores the x+9 in the original denominator; and a = 8x + 9 represents a completely different operation (multiplication and addition) rather than division by x+9.