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

The solution to sqrt(3x+7)>sqrt(x-2) is x>= 2

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sqrt(3x+7)>sqrt(x-2)

3 x + 7 > x - 2

x \geq 2

Interval Notation

[2, \infty)

Solution steps

3 x + 7 > x - 2

Square both sides

(3 x + 7)^{2} > (x - 2)^{2}

Simplify

3 x + 7 > x - 2

3 x + 7 > x - 2 : x > - \frac{9}{2}

x > - \frac{9}{2}

Find singularity points

Find non-negative values for radicals:

x \geq 2

Combine the intervals

x > - \frac{9}{2} and x \geq 2

Merge Overlapping Intervals

x \geq 2

3 x^{2} - 22 x + 39

∣ 5 x - 3 ∣ = 7

3 (\frac{5 n}{11})^{1.5}

3 x^{3} y^{2} z + 6 x^{2} y

248 - 3