Question
4)) Select the expressions that are equivalent to \( -3(t-4) \). \( -4(-3+t) \) \( (-4+t) \cdot-3 \) \( -3(-4+t) \)
Ask by Deleon Burns. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expressions equivalent to \( -3(t - 4) \) are \( (-4 + t) \cdot -3 \) and \( -3(-4 + t) \).
Solution
To determine which expressions are equivalent to \( -3(t - 4) \), let's first simplify the original expression:
\[
-3(t - 4) = -3t + 12
\]
Now, let's evaluate each of the given expressions:
1. **\( -4(-3 + t) \)**
\[
-4(-3 + t) = -4(t - 3) = -4t + 12
\]
This simplifies to \( -4t + 12 \), which is **not** the same as \( -3t + 12 \).
2. **\( (-4 + t) \cdot -3 \)**
\[
(-4 + t) \cdot -3 = -3(t - 4) = -3t + 12
\]
This directly matches the original expression \( -3t + 12 \).
3. **\( -3(-4 + t) \)**
\[
-3(-4 + t) = -3(t - 4) = -3t + 12
\]
This also directly matches the original expression \( -3t + 12 \).
**Conclusion:** The expressions that are equivalent to \( -3(t - 4) \) are:
- \( (-4 + t) \cdot -3 \)
- \( -3(-4 + t) \)
**Therefore, the correct equivalent expressions are the second and third options.**
**Answer:** Both the second and third expressions are equivalent to –3(t – 4).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find expressions equivalent to \( -3(t-4) \), we can distribute the \(-3\) across the parentheses. This gives us: \[ -3(t-4) = -3t + 12 \] Now, let’s evaluate each option: 1. For \( -4(-3+t) \), distribute \(-4\): \[ -4(-3+t) = 12 - 4t, \] which is **not equivalent**. 2. For \( (-4+t) \cdot -3 \): \[ (-4+t) \cdot -3 = 12 - 3t, \] which is also **not equivalent**. 3. For \( -3(-4+t) \): \[ -3(-4+t) = 12 - 3t, \] which again is **not equivalent**. Thus, none of the provided expressions are equivalent to \( -3(t-4) \).
