To solve the inequality \( 5 < 12y - 7 \), Kirk would follow these steps:
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Add 7 to both sides: This helps isolate the term with the variable. \[ 5 + 7 < 12y \] which simplifies to: \[ 12 < 12y \]
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Divide both sides by 12: This step helps solve for \( y \) by isolating it. Remember that since we are dividing by a positive number, the inequality direction remains the same. \[ \frac{12}{12} < y \] which simplifies to: \[ 1 < y \] or equivalently, \[ y > 1 \]
The solution set of the inequality is \( y > 1 \). Kirk’s steps involved first isolating the term with the variable and then solving for \( y \) while maintaining the direction of the inequality.