To help Tucker decide on his first step in solving the equation \( 5x + 3 = 6x + 1 \), we can analyze the equation and determine which step would be most effective.
The goal in solving for \( x \) is to isolate the variable on one side of the equation. In this case, Tucker has two options for the first step:
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Add 5 negative \( x \)-tiles (which would essentially mean moving \( 6x \) from the right side to the left side): This would lead to rearranging the equation as follows: \[ 5x + 3 - 6x = 1 \] Simplifying this would give: \[ -x + 3 = 1 \] This is a valid step and can lead to isolating \( x \).
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Add 1 negative unit tile (which means subtracting 1 from both sides): This would lead to: \[ 5x + 3 - 1 = 6x + 1 - 1 \] Simplifying this would give: \[ 5x + 2 = 6x \] This is also a valid step and can help isolate \( x \).
Both steps are valid, but one might be simpler or more intuitive depending on Tucker's understanding of the equation.
Advice:
It might be easier for Tucker to start by moving the \( 6x \) term to the left side by adding \( -6x \) (or "5 negative \( x \)-tiles") to both sides. This approach reduces the number of terms associated with \( x \) right away, potentially making the next steps more straightforward.
After moving \( 6x \) to the left, he can easily combine like terms and continue to solve for \( x \).
So, I would suggest that Tucker adds 5 negative \( x \)-tiles to both sides to start. It usually helps to eliminate the variable term on one side as a first step.
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