Question

Sqrt(2x-6)=3-x Solve for x

Answer 1

Answer:

x = 3

Step-by-step explanation:

$\sqrt{2x - 6} = 3 - x$

Square both sides of the equation

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

$x^{2} - 8x + 15 = 0$

(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 $\sqrt{2x - 6} = \sqrt{2(3) - 6} = \sqrt{6 - 6} = \sqrt{0} = 0$  and 3 - x = 3 - 3 = 0

So 3 satisfies the original.

If x = 5, then $\sqrt{2(5) - 6} = \sqrt{10 - 6} = \sqrt{4} = 2$,  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.