Question

1. √(x + 6) = -8
x=?

2. 4√(2x - 3) < 12
solve the inequality

3. 4 ≥ √(6x - 12) - 8
solve the inequality

4. √(3x - 5) = x - 3
x=?

5. √(4 - x) ≥ √(3x + 4)
solve the inequality

6. x + 3 = √(5x + 4) + 1
x=?

Answer 1

I will be happy to critique your work.

Answer 2

I will do #2 and #4, you can try the rest by following the same method.

#2.
4√(2x - 3) < 12
√(2x - 3) < 3 , now square both sides
2x - 3 < 9
2x < 12
x < 6

since we squared, we have to check our answer.
try x=2
LS = 4√(2(2)- 3) = 4
RS = 12
Is 4 < 12 ? Yes!

so x < 6

#4
√(3x - 5) = x - 3
square both sides
3x-5 = x^2 - 6x + 9
x^2 - 9x + 12 = 0
(x-7)(x-2) = 0
x = 7 or x = 2

checking:
if x=7
LS = √(21-5) = 4
RS = 7-3 = 4 , YES

if x=2
LS = √(4-1) = 1
RS = 2-3 = -1 , NO

so x = 7