What is the answer to sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16) ?

The answer to sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16) is x=4

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sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16)

2 x - 4 - 3 x - 12 = 5 x - 16

x = 4

Solution steps

2 x - 4 - 3 x - 12 = 5 x - 16

Square both sides:

5 x - 2 2 x - 4 3 x - 12 - 16 = 5 x - 16

5 x - 2 2 x - 4 3 x - 12 - 16 = 5 x - 16

Subtract

5 x - 16

from both sides

5 x - 2 2 x - 4 3 x - 12 - 16 - (5 x - 16) = 5 x - 16 - (5 x - 16)

Simplify

- 2 2 x - 4 3 x - 12 = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x - 4 = 0 or 3 x - 12 = 0

Solve

2 x - 4 = 0 : x = 2

Solve

3 x - 12 = 0 : x = 4

x = 2, x = 4

Verify Solutions:

x = 2

False

, x = 4

True

The solution is

x = 4

x - 3 + 4 = 1

x + 4 = - 4

1 + 7 - 6 x = - 2 x

x^{2} + 2 x + 3 = 4 - x^{2}

What is the answer to sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16) ?
The answer to sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16) is x=4
Solve for x: sqrt(2x-4)-sqrt(3x-12)=sqrt(5x-16)
The solution is x=4