Question

What value is equivalent to the expression below?
3(1/4 - 2) + |-7|

Answer 1

What value is equivalent to the expression below?
3(1/4 - 2) + |-7|


A. 5 3/4
B. -12 1/4
C. -8 1/4
D. 1 3/4

Answer 2

Let's evaluate the expression step-by-step:

1. Start with the expression:
\[
3\left(\frac{1}{4} - 2\right) + |-7|
\]

2. Calculate \(\frac{1}{4} - 2\):
\[
\frac{1}{4} - 2 = \frac{1}{4} - \frac{8}{4} = \frac{1 - 8}{4} = \frac{-7}{4}
\]

3. Now, substitute this result back into the expression:
\[
3\left(\frac{-7}{4}\right) + |-7|
\]

4. Now calculate \(3 \left(\frac{-7}{4}\right)\):
\[
3 \cdot \frac{-7}{4} = \frac{-21}{4}
\]

5. Next, calculate \( |-7| \):
\[
|-7| = 7
\]

6. Now substitute back into the expression:
\[
\frac{-21}{4} + 7
\]

7. Convert \(7\) into a fraction with a denominator of \(4\):
\[
7 = \frac{28}{4}
\]

8. Now add the fractions:
\[
\frac{-21}{4} + \frac{28}{4} = \frac{-21 + 28}{4} = \frac{7}{4}
\]

Thus, the value equivalent to the original expression is:
\[
\boxed{\frac{7}{4}}
\]

Answer 3

Let's evaluate the expression again to match it with the answer choices provided:

The expression is:

\[
3\left(\frac{1}{4} - 2\right) + |-7|
\]

1. First, calculate \(\frac{1}{4} - 2\):
\[
\frac{1}{4} - 2 = \frac{1}{4} - \frac{8}{4} = \frac{1 - 8}{4} = \frac{-7}{4}
\]

2. Next, multiply by 3:
\[
3\left(\frac{-7}{4}\right) = \frac{-21}{4}
\]

3. Calculate \( |-7| \):
\[
|-7| = 7
\]

4. Now we can combine the two results:
\[
\frac{-21}{4} + 7
\]

5. Convert \( 7 \) into a fraction with a common denominator of \( 4 \):
\[
7 = \frac{28}{4}
\]

6. Now add the two fractions:
\[
\frac{-21}{4} + \frac{28}{4} = \frac{-21 + 28}{4} = \frac{7}{4}
\]

The value \(\frac{7}{4}\) can be expressed as a mixed number:
\[
\frac{7}{4} = 1\frac{3}{4}
\]

Thus, the final answer is:
\[
\boxed{1 \frac{3}{4}}
\]

According to your answer choices, it corresponds to **D. 1 3/4**.