Question
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Answer
The equation \(6(y+-1)=6y-6\) is true for all real numbers \(y\).
Solution
Solve the equation \( 6(y+-1)=6 y-6 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(6\left(y-1\right)=6y-6\)
- step1: Expand the expression:
\(6y-6=6y-6\)
- step2: The statement is true:
\(y \in \mathbb{R}\)
The solution to the equation \(6(y+-1)=6y-6\) is \(y \in \mathbb{R}\), which means that \(y\) can be any real number. Therefore, the equation is true for all real values of \(y\).
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Simplify this solution Bonus Knowledge
Let's simplify the equation by distributing the \( 6 \) on the left side: \[ 6y - 6 = 6y - 6 \] Now, if we subtract \( 6y \) from both sides, we get: \[ -6 = -6 \] This indicates that the equation is an identity, meaning it holds true for all values of \( y \). So, any value of \( y \) will satisfy this equation! How convenient is that? If you want to explore further, you can try substituting different values for \( y \) into the original equation and verify that both sides remain equal every time. It's a great way to see algebra in action and discover how sometimes equations can be true universally!
