Question

Use the properties of equality to solve the equation 7x - 4 + x = 12. State which property justifies your first step

and why you chose it. Check your solution,

Answer 1

x=2

Explanation:

Explanation in picture

Answer 2

x = 2

Explanation:

8x = 16 . . . . . addition property of equality (add 4 to both sides). This step separates variable terms from constant terms.

x = 2 . . . . . . . multiplication property of equality (multiply both sides by 1/8)

_____

Strictly speaking, combining like terms involves the distributive property of multiplication over addition, and the closure of the set of real numbers. It does not involve a property of equality, as such. The steps shown above have "combining like terms" as an "invisible" step, just as writing out ...

7x -4 +x +4 = 12 +4

is an "invisible" step. It is described as "add 4 to both sides". The result of that step is shown.