What is the answer to sqrt((x-3)^2)=3-x ?

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

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sqrt((x-3)^2)=3-x

(x - 3)^{2} = 3 - x

x \leq 3

Solution steps

(x - 3)^{2} = 3 - x

Square both sides:

(x - 3)^{2} = 9 - 6 x + x^{2}

(x - 3)^{2} = 9 - 6 x + x^{2}

Solve

(x - 3)^{2} = 9 - 6 x + 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 - 6 = 0

13 - x^{2} + x = 5

3 x - 5 - x + 2 = 1

x - x - 2 = 2

7 x + 11 = 4 x + 1 + 2

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