What is sqrt(3x+9)-2<7 ?

The solution to sqrt(3x+9)-2<7 is -3<= x<24

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sqrt(3x+9)-2<7

3 x + 9 - 2 < 7

- 3 \leq x < 24

Interval Notation

[- 3, 24)

Solution steps

3 x + 9 - 2 < 7

Move

2

to the right side

3 x + 9 < 9

Square both sides

(3 x + 9)^{2} < 9^{2}

Simplify

3 x + 9 < 81

3 x + 9 < 81 : x < 24

x < 24

Find singularity points

Find non-negative values for radicals:

x \geq - 3

Combine the intervals

x < 24 and x \geq - 3

Merge Overlapping Intervals

- 3 \leq x < 24

3 (k - 2) - 4 k (k - 2)

(\frac{1}{3})^{- 3}

7 x (x - 3) = 0

- 5 + \frac{n}{3} = 0

x^{2} - 16 x - 63 = 0