The perimeter is the sum of all the sides of a geometric figure, so
[tex]\begin{gathered} (x+4)+x+(x+4)+x<120 \\ x+4+x+x+4+x<120 \\ 4x+8<120 \end{gathered}[/tex]
To resolve this inequality you can first subtract 8 from both sides
[tex]\begin{gathered} 4x+8-8<120-8 \\ 4x<112 \end{gathered}[/tex]
Then you divide by 4 on both sides of the inequality
[tex]\begin{gathered} \frac{4x}{4}<\frac{112}{4} \\ x<28 \end{gathered}[/tex]
Therefore, for the perimeter of the rectangle to be less than 120, its shortest side must measure less than 28.
