Given:
Consider the sides of the triangle are 4x+10, 2x-5 and 18 (in feet).
Perimeter of this triangle is to be no more than 77 feet.
To find:
The inequality and solution of the inequality.
Solution:
Perimeter of a triangle is the sum of all side.
Perimeter of given triangle [tex]=(4x+10)+(2x-5)+18[/tex]
Perimeter of this triangle is to be no more than 77 feet. It means perimeter must be less than or equal to 77.
[tex](4x+10)+(2x-5)+18\leq 77[/tex]
[tex](4x+2x)+(10-5+18)\leq 77[/tex]
[tex]6x+23\leq 77[/tex]
[tex]6x\leq 77-23[/tex]
[tex]6x\leq 54[/tex]
Divide both sides by 6.
[tex]x\leq \dfrac{54}{6}[/tex]
[tex]x\leq 9[/tex]
Therefore, the required inequality is [tex](4x+10)+(2x-5)+18\leq 77[/tex] and the solution is [tex]x\leq 9[/tex].
