Answer:
x = 3
Step-by-step explanation:
[tex]\sqrt{2x - 6} = 3 - x[/tex]
Square both sides of the equation
[tex]2x - 6 = (3 - x)^{2} = 9 - 6x + x^{2} \\[/tex]
[tex]x^{2} - 8x + 15 = 0\\[/tex]
(x - 3)(x - 5) = 0
x = 3 or 5
Now, you must always check your results because a result may not satisfy the original equation.
If x = 3, then [tex]\sqrt{2x - 6} = \sqrt{2(3) - 6} = \sqrt{6 - 6} = \sqrt{0} = 0[/tex] and 3 - x = 3 - 3 = 0
So 3 satisfies the original.
If x = 5, then [tex]\sqrt{2(5) - 6} = \sqrt{10 - 6} = \sqrt{4} = 2[/tex], but 3 - x = 3 - 5 = -2. Therefore, 5 does NOT satisfy the original equation.
That means that x = 3 is the solution to the equation.
