Question

which expression is equivalent to 1/2b - 15?

a. 1/2(b+ 30)

b. -1/2(b - 30)

c. -1/2(b + 30)

d. 1/2(b - 30)

Answer 1

To find the expression equivalent to \( \frac{1}{2}b - 15 \), let's look at each option and see if it simplifies to the original expression.

**Option a: \( \frac{1}{2}(b + 30) \)**

\[
\frac{1}{2}(b + 30) = \frac{1}{2}b + \frac{1}{2} \times 30 = \frac{1}{2}b + 15
\]
This does not equal \( \frac{1}{2}b - 15 \).

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**Option b: \( -\frac{1}{2}(b - 30) \)**

\[
-\frac{1}{2}(b - 30) = -\frac{1}{2}b + \frac{1}{2} \times 30 = -\frac{1}{2}b + 15
\]
This does not equal \( \frac{1}{2}b - 15 \).

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**Option c: \( -\frac{1}{2}(b + 30) \)**

\[
-\frac{1}{2}(b + 30) = -\frac{1}{2}b - \frac{1}{2} \times 30 = -\frac{1}{2}b - 15
\]
This does not equal \( \frac{1}{2}b - 15 \).

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**Option d: \( \frac{1}{2}(b - 30) \)**

\[
\frac{1}{2}(b - 30) = \frac{1}{2}b - \frac{1}{2} \times 30 = \frac{1}{2}b - 15
\]
This is equal to \( \frac{1}{2}b - 15 \).

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Thus, the expression equivalent to \( \frac{1}{2}b - 15 \) is **Option d: \( \frac{1}{2}(b - 30) \)**.