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We are told that the dog should weigh less than $65$ pounds. The phrase "less than" can be algebraically expressed using the symbol $<.$ Now we can write an inequality that describes the desired weight for the dog. $\begin{gathered} \text{Desired weight}< 65 \end{gathered}$ The current weight of the dog is $80$ pounds and she is expected to lose $1.25$ pounds per week on the new diet. If we call the number of weeks the dog has to diet $x,$ we can write the left-hand side of the inequality. $\begin{gathered} 80-1.25x< 65 \end{gathered}$ By solving for $x$ we can find how many weeks it will take for the dog to reach her dream weight.
$80-1.25x<65$
$\text{-} 1.25x<\text{-} 15$
$x> \dfrac{\text{-} 15}{\text{-} 1.25}$
$x>12$
It's going to take more than $12$ weeks for the dog to reach a healthy weight.