Pregunta
Solve for \( y \). \[ -7=-\frac{9}{y} \] Simplify your answer as much as possible.
Ask by Willis Li. in the United States
Feb 19,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( y = \frac{9}{7} \)
Solución
Solve the equation \( -7=-\frac{9}{y} \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(-7=-\frac{9}{y}\)
- step1: Find the domain:
\(-7=-\frac{9}{y},y\neq 0\)
- step2: Swap the sides:
\(-\frac{9}{y}=-7\)
- step3: Rewrite the expression:
\(\frac{-9}{y}=-7\)
- step4: Cross multiply:
\(-9=y\left(-7\right)\)
- step5: Simplify the equation:
\(-9=-7y\)
- step6: Evaluate:
\(9=7y\)
- step7: Swap the sides:
\(7y=9\)
- step8: Divide both sides:
\(\frac{7y}{7}=\frac{9}{7}\)
- step9: Divide the numbers:
\(y=\frac{9}{7}\)
- step10: Check if the solution is in the defined range:
\(y=\frac{9}{7},y\neq 0\)
- step11: Find the intersection:
\(y=\frac{9}{7}\)
The solution to the equation \(-7=-\frac{9}{y}\) is \(y=\frac{9}{7}\) or \(y=1.285714\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
To solve for \( y \), first, we can eliminate the negative sign by multiplying both sides of the equation by -1: \[ 7 = \frac{9}{y} \] Next, we can cross-multiply to get rid of the fraction: \[ 7y = 9 \] Now, to isolate \( y \), divide both sides by 7: \[ y = \frac{9}{7} \] Thus, the simplified answer is \[ y = \frac{9}{7}. \]
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