algebra
posted by irina .
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=?

I will be happy to critique your work.

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
3x5 = x^2  6x + 9
x^2  9x + 12 = 0
(x7)(x2) = 0
x = 7 or x = 2
checking:
if x=7
LS = √(215) = 4
RS = 73 = 4 , YES
if x=2
LS = √(41) = 1
RS = 23 = 1 , NO
so x = 7
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