This is a one step addition inequalities

r is less than or equal to -28

Step-by-step explanation:

(-2r-9) +14 +3r ≤ 11-34

Combine like terms

1r+5 ≤ -23

Subtract 5 to isolate variable

1r ≤ -28

Divide to get r isolated

r ≤ -28

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