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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.
It's going to take more than $12$ weeks for the dog to reach a healthy weight.

$80-1.25x<65$

SubIneq$\text{LHS}-80<\text{RHS}-80$

$\text{-} 1.25x<\text{-} 15$

DivNegIneqDivide by $\text{-} 1.25$ and flip inequality sign

$x> \dfrac{\text{-} 15}{\text{-} 1.25}$

DivNegNeg$\dfrac{\text{-} a}{\text{-} b}=\dfrac{a}{b}$

$x>12$