Question
What is \( 6 z-2 y-8 z+5 y-4+z \) written in simplest form? \( -3 y+z-4 \) \( 7 y+z-4 \) \( 15 z-3 y-4 \) \( 3 y-z-4 \)
Ask by Ford Zimmerman. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( 3y - z - 4 \).
Solution
To simplify the expression \( 6z - 2y - 8z + 5y - 4 + z \), follow these steps:
1. **Combine like terms for \( z \):**
\[
6z - 8z + z = (6 - 8 + 1)z = (-2 + 1)z = -z
\]
2. **Combine like terms for \( y \):**
\[
-2y + 5y = ( -2 + 5)y = 3y
\]
3. **Combine the constant terms:**
\[
-4
\]
Putting it all together, the simplified form of the expression is:
\[
3y - z - 4
\]
**Correct Answer:**
\[
3y - z - 4
\]
This corresponds to the fourth option provided:
- \( 3 y - z -4 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To simplify the expression \( 6z - 2y - 8z + 5y - 4 + z \), we can combine like terms. First, let's group the \( z \) terms: \( 6z - 8z + z = (6 - 8 + 1)z = -1z\) or simply \(-z\). Next, we combine the \( y \) terms: \(-2y + 5y = (5 - 2)y = 3y\). Now, putting it all together, we have: \(-z + 3y - 4\). So, the final expression in simplest form is \( 3y - z - 4 \). The correct answer is \( 3y - z - 4 \).
