Pregunta
Which of the following equations is equivalent to \( 7=2 y+9 ? \)
Ask by Owen Weber. in Italy
Nov 12,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Two equivalent equations are \( -2 = 2y \) and \( y = -1 \).
Solución
To find an equivalent equation to \( 7 = 2y + 9 \), you can perform the same operation on both sides of the equation without changing its solution. Here are a few operations you can use:
1. Subtract 9 from both sides:
\[ 7 - 9 = 2y + 9 - 9 \]
\[ -2 = 2y \]
2. Divide both sides by 2:
\[ \frac{-2}{2} = \frac{2y}{2} \]
\[ -1 = y \]
So, two equivalent equations to \( 7 = 2y + 9 \) are:
\[ -2 = 2y \]
\[ y = -1 \]
If you have a list of equations to choose from, you would need to compare them to these forms to determine which ones are equivalent.
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Simplifique esta solución Beyond the Answer
To solve for \( y \), let's first isolate it in the equation \( 7 = 2y + 9 \). Start by subtracting 9 from both sides: \( 7 - 9 = 2y \), which simplifies to \( -2 = 2y \). Now, divide both sides by 2 to get \( y = -1 \). Now, if we set it up in another way, we can rewrite the original equation as \( 2y = 7 - 9 \), which also leads to the conclusion \( 2y = -2 \) and again to \( y = -1 \). So, the equivalent equation could also be expressed as \( 2y = -2 \). So, both \( y = -1 \) and \( 2y = -2 \) are equivalent forms when working with the original equation!
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