How do you Solve this equation sqrt(3x+7) + 3=6?

sqrt(3x+7) + 3=6
sqrt(3x+7)=6-3
sqrt(3x+7) =3
squaring both the sides
3x+7=3^2=9
3x=9-7
3x=2
x=2/3

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we've a linear equation the following. The question is searching you: what style situations 7 = 40 2? the obtrusive answer is 6, excellent? So, x = 6...determination B to remedy it the algebra way, divide both area of the equation through 7. 7x = 40 2 x = 40 2 divided through 7 x = 6

√(3x + 7) + 3 = 6
√(3x + 7) = 6 - 3
3x + 7 = 3^2
3x + 7 = 9
3x = 9 - 7
x = 2/3

3x + 7= 9
3x = 2
x = 2/3

sqrt(3x + 7) + 3 = 6
sqrt(3x + 7) = 3

Square both sides,

3x + 7 = 9

Solve for x as normal.

3x = 2
x = 2/3

However, know that with radical equations, each evaluated solution may not necessarily work. This is why we must plug into the original to check for extraneous solutions.

If x = 2/3, and our equation is sqrt(3x + 7) + 3 = 6, then

LHS = sqrt(3x + 7) + 3
= sqrt(3[2/3] + 7) + 3
= sqrt(2 + 7) + 3
= sqrt(9) + 3
= 3 + 3
= 6 = RHS

Therefore, it works.