Question
By what number should \( (-6)^{-1} \) be mult so that the product becomes \( g^{-1} \)
Ask by Bernard Weston. in India
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number to multiply \( (-6)^{-1} \) by to get \( g^{-1} \) is \( -\frac{6}{g} \).
Solution
To determine the number \( x \) that you need to multiply by \( (-6)^{-1} \) to get \( g^{-1} \), you can set up the equation as follows:
\[
x \times (-6)^{-1} = g^{-1}
\]
Let's solve for \( x \):
1. **Express \( (-6)^{-1} \) as a fraction:**
\[
(-6)^{-1} = \frac{1}{-6} = -\frac{1}{6}
\]
2. **Substitute into the equation:**
\[
x \times \left(-\frac{1}{6}\right) = \frac{1}{g}
\]
3. **Solve for \( x \):**
\[
x = \frac{\frac{1}{g}}{-\frac{1}{6}} = \frac{1}{g} \times \left(-6\right) = -\frac{6}{g}
\]
So, the number you need to multiply by \( (-6)^{-1} \) to obtain \( g^{-1} \) is:
\[
x = -\frac{6}{g}
\]
**Final Answer:**
After simplifying, the required number is –6 divided by g. Thus,
x = −6 ⁄ g
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find out by what number \( (-6)^{-1} \) should be multiplied to produce \( g^{-1} \), we start with \( (-6)^{-1} = -\frac{1}{6} \). You want to determine the multiplier \( x \) so that: \[ (-6)^{-1} \cdot x = g^{-1} \] Rearranging this gives us: \[ x = g^{-1} \cdot (-6) \] In simpler terms, you can express the multiplier \( x \) as \( -6g^{-1} \). So, if you multiply \( -\frac{1}{6} \) by \( -6g^{-1} \), you’ll find your requisite product to yield \( g^{-1} \)! Now you can take your newfound knowledge and apply it in various mathematical contexts or even derive further equations using this concept.
