Question

What is the justification for each step in solving the inequality?

75x+35≥7(11x+9)+475x+35≥7(11x+9)+4

75x+35≥7(11x+9)+475x+35≥7(11x+9)+4

75x+35≥77x+63+475x+35≥77x+63+4

75x+35≥77x+6775x+35≥77x+67

−2x+35≥67−2x+35≥67 −2x≥32−2x≥32

x≤−16x≤−16

Answer 1

Given

Distributive Property

Combine like terms

Subtraction Property of Order

Subtraction Property of Order

Division Property of Order

I hope this helps!

Answer 2

75x+35≥7(11x+9)+475x+35≥7(11x+9)+4

75x+35≥77x+63+475x+35≥77x+63+4 [expand all blackets]

75x+35≥77x+6775x+35≥77x+67 [collect like terms]

−2x+35≥67−2x+35≥67 −2x≥32−2x≥32 [subtract 77x through]

x≤−16x≤−16 [subtract 35 through and divide through by 2]