Question
The coefficient is \( -\frac{6}{1} \). What value can you multiply both sides of the equation by so that the coefficient becomes 1 ?
Ask by Campos Harris. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Multiply both sides by \(-\frac{1}{6}\).
Solution
To change the coefficient from \(-\frac{6}{1}\) (which is \(-6\)) to \(1\), you need to multiply both sides of the equation by a value that will cancel out the \(-6\).
Here's how you can determine that value:
1. **Desired Coefficient:** You want the new coefficient to be \(1\).
2. **Current Coefficient:** The current coefficient is \(-6\).
3. **Multiplicative Inverse:** To change \(-6\) to \(1\), you multiply by the inverse of \(-6\), which is \(-\frac{1}{6}\).
**Mathematically:**
\[
-6 \times \left(-\frac{1}{6}\right) = 1
\]
**Therefore, you should multiply both sides of the equation by \(-\frac{1}{6}\).**
**Answer:** Multiply both sides by –1⁄6.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To transform the coefficient \( -\frac{6}{1} \) into 1, you need to multiply both sides of the equation by the reciprocal of the coefficient, which is \( -\frac{1}{6} \). When you multiply \( -\frac{6}{1} \) by \( -\frac{1}{6} \), you get 1, effectively simplifying your equation! On a fun note, this technique of multiplying by the reciprocal is a superhero move in algebra! It’s like turning a heavy weightlifting task (a large coefficient) into a smooth glide across the finish line (reaching that desired coefficient of 1) – what an empowering transformation!
