algebra

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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=?

  • algebra -

    I will be happy to critique your work.

  • algebra -

    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

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