What is the value of x?

x = 20

Step-by-step explanation:

The angles are vertical angles which means they are equal

x+40 = 3x

Subtract x from each side

x+40-x = 3x-x

40 = 2x

Divide by 2

40/2 = 2x/2

20 =x

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is