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embizze eNotes educator| Certified Educator

Solve 9x-11=x+5 :

The goal is to write a set of equivalent equations ( each has the same solution set) ending with the simplest form of x= the solution(s).

Equivalent equations can be formed if we use the properties of equality including the addition, subtraction, multiplication, and division properties.

9x-11=x+5  Subtract x from both sides (Subtraction prop of =)

8x-11=0+5  0+5=5 (additive identity property)

8x-11=5      Add 11 to both sides (Addition prop of =)

8x+0=16     8x+0=8x (Additive identity property)

8x=16         Divide both sides by 8 (Division prop of =)

1x=2           1x=x (Multiplicative identity property)



The solution to 9x-11=x+5 is x=2


Check by substituting the x-value into the original equation to make sure it makes a true statement:

9(2)-11=18-11=7=2+5 so the solution is indeed 2.