What is the answer to sqrt((2x-6)^2)=6-2x ?

The answer to sqrt((2x-6)^2)=6-2x is x<= 3

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sqrt((2x-6)^2)=6-2x

(2 x - 6)^{2} = 6 - 2 x

x \leq 3

Solution steps

(2 x - 6)^{2} = 6 - 2 x

Square both sides:

(2 x - 6)^{2} = 36 - 24 x + 4 x^{2}

(2 x - 6)^{2} = 36 - 24 x + 4 x^{2}

Solve

(2 x - 6)^{2} = 36 - 24 x + 4 x^{2} :

True for all

x

True for all x

Verify Solutions:

x < 3

True

, x = 3

True

, x > 3

False

The solution is

x \leq 3

x + x = 380

x^{2} + 4 x - 1 = 2 x

What is the answer to sqrt((2x-6)^2)=6-2x ?
The answer to sqrt((2x-6)^2)=6-2x is x<= 3
Solve for x: sqrt((2x-6)^2)=6-2x
The solution is x<= 3