What is the answer to sqrt(x+3)-sqrt(x-2)=sqrt(6x-11) ?

The answer to sqrt(x+3)-sqrt(x-2)=sqrt(6x-11) is x= 7/3

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sqrt(x+3)-sqrt(x-2)=sqrt(6x-11)

x + 3 - x - 2 = 6 x - 11

x = \frac{7}{3}

Decimal

x = 2.33333 \dots

Solution steps

x + 3 - x - 2 = 6 x - 11

Remove square roots

4 x^{2} + 4 x - 24 = 16 x^{2} - 96 x + 144

Solve

4 x^{2} + 4 x - 24 = 16 x^{2} - 96 x + 144 : x = \frac{7}{3}, x = 6

x = \frac{7}{3}, x = 6

Verify Solutions:

x = \frac{7}{3}

True

, x = 6

False

The solution is

x = \frac{7}{3}

42 - 6 x = x - 7

9 x + 9 = x + 1

x + 7 - 3 x = 1

7 x + 18 = x + 4

x^{\frac{2}{3}} - 2 x^{\frac{1}{3}} - 15 = 0

What is the answer to sqrt(x+3)-sqrt(x-2)=sqrt(6x-11) ?
The answer to sqrt(x+3)-sqrt(x-2)=sqrt(6x-11) is x= 7/3
Solve for x: sqrt(x+3)-sqrt(x-2)=sqrt(6x-11)
The solution is x= 7/3