solve each equation. check for extraneous solution.

sqrt(3x+4)-sqrt(2x-7)=3

please show work!!!!!

Follow the same steps suggested by Steve in your previous post

or

take the negative term to the right side, then square
collect all like terms, isolate the square root term and square again.

Steve can't teach well

To solve the equation sqrt(3x+4) - sqrt(2x-7) = 3 and check for extraneous solutions, follow these steps:

Step 1: Isolate one of the radicals by moving the other one to the other side of the equation.
sqrt(3x+4) = sqrt(2x-7) + 3

Step 2: Square both sides of the equation to eliminate the radicals.
(3x+4) = (2x-7) + 6sqrt(2x-7) + 9

Step 3: Simplify the equation.
3x + 4 = 2x - 7 + 6sqrt(2x-7) + 9

Step 4: Combine like terms.
x + 6 = 6sqrt(2x-7)

Step 5: Square both sides again to eliminate the remaining square root.
(x + 6)^2 = (6sqrt(2x-7))^2
x^2 + 12x + 36 = 36(2x - 7)

Step 6: Expand and simplify the equation.
x^2 + 12x + 36 = 72x - 252

Step 7: Move all terms to one side to create a quadratic equation.
x^2 - 60x + 288 = 0

Step 8: Solve the quadratic equation by factoring, completing the square, or using the quadratic formula.
In this case, the equation can be factored:
(x - 6)(x - 48) = 0

Therefore, x - 6 = 0 or x - 48 = 0
Solving for x gives us x = 6 or x = 48.

Step 9: Check for extraneous solutions by substituting the potential solutions back into the original equation.
For x = 6:
sqrt(3(6)+4) - sqrt(2(6)-7) = 3
sqrt(18+4) - sqrt(12-7) = 3
sqrt(22) - sqrt(5) = 3
4.69 - 2.24 = 3
2.45 = 3 (Not true)

For x = 48:
sqrt(3(48)+4) - sqrt(2(48)-7) = 3
sqrt(144+4) - sqrt(96-7) = 3
sqrt(148) - sqrt(89) = 3
12.17 - 9.43 = 3
2.74 = 3 (Not true)

Since the potential solutions for x = 6 and x = 48 do not satisfy the original equation, there are no valid solutions.