What is 1/2 sqrt(x+9)<2 ?

The solution to 1/2 sqrt(x+9)<2 is -9<= x<7

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1/2 sqrt(x+9)<2

\frac{1}{2} x + 9 < 2

- 9 \leq x < 7

Interval Notation

[- 9, 7)

Solution steps

\frac{1}{2} x + 9 < 2

Multiply both sides by

2

2 \cdot \frac{1}{2} x + 9 < 2 \cdot 2

Simplify

x + 9 < 4

Square both sides

(x + 9)^{2} < 4^{2}

Simplify

x + 9 < 16

Move

9

to the right side

x < 7

Find singularity points

Find non-negative values for radicals:

x \geq - 9

Combine the intervals

x < 7 and x \geq - 9

Merge Overlapping Intervals

- 9 \leq x < 7

x^{2} + 12 x - 1 = 9

2 y = 6

1 + x - 53 = x^{2} - 2 x - 152 x

- 16 x > - 80

6 x^{2} + 48 x