Answer:
[tex]f(x)<-2x+6[/tex]
[tex]g(x) \leq x+2[/tex]
Step-by-step explanation:
step 1
Fin the equation of the linear inequality f(x)
we know that
The solution of the linear inequality f(x) is the shaded area below the dashed line
The y-intercept of the dashed line is (0,6)
The x-intercept of the dashed line is (3,0)
The slope of the dashed line is negative and its value is equal to
[tex]m=(0-6)\(3-0)=-2[/tex]
The linear function f(x) in slope intercept form is equal to
[tex]f(x)=-2x+6[/tex]
therefore
The linear inequality f(x) is equal to
[tex]f(x)<-2x+6[/tex] ----> is < because is a dashed line and the shaded area is below the line
step 2
Fin the equation of the linear inequality g(x)
we know that
The solution of the linear inequality g(x) is the shaded area below the solid line
The y-intercept of the solid line is (0,2)
The x-intercept of the solid line is (-2,0)
The slope of the solid line is positive and its value is equal to
[tex]m=(0-2)\(-2-0)=1[/tex]
The linear function g(x) in slope intercept form is equal to
[tex]g(x)=x+2[/tex]
therefore
The linear inequality g(x) is equal to
[tex]g(x) \leq x+2[/tex] ----> is ≤ because is a solid line and the shaded area is below the line
therefore
The system of inequalities is equal to
[tex]f(x)<-2x+6[/tex]
[tex]g(x) \leq x+2[/tex]
